"Native [language, etc.]" is not a technical term, and it's more of a general description.

In the strictest sense, a native speaker is a monolingual who has spoken the language from birth, continuously, for their whole lives. Maybe even an adult. And maybe even an educated individual.

But it depends on who is using the term. Almost all linguists would agree that a native speaker does not need to be educated. Some might also allow for "heritage" languages, for individuals who have now lost some ability (or never had full knowledge) in a language, but who learned it as a child, usually from their parents. (For example, a child of Chinese immigrants in an English speaking country-- the child would know and use some Chinese for a few years then during school learn and use English and as an adult maybe forget almost all knowledge of Chinese.)

And certainly children can be considered [child] native speakers of a language.

But then there's the question of an age. The general distinction is between child and adult. Children became native speakers. Adults do not. But at what age is this distinguished? Unclear. The idea of a "critical period" for language learning is that at some point, something is different about children who grow up and become adults (biological? behavioral? neurological? social?) and they can no longer learn a language in the same way and do not become native speakers. The critical period is said to begin around 2-3 years of age (no infants are fully competent native speakers of a language yet, and are arguably not capable of learning a language fully yet), and it is said to end some time around puberty (about 12) or maybe a little earlier (9-10). Some studies have said as late as 14-15, and others have said as early as 5. It depends on the domain as well: phonology (sounds) might be earlier than syntax ('grammar' in the traditional sense). And it has also been pointed out that at least a few things (such as in syntax, some particularly complicated kinds of sentences) are not developed until up to age 15, although by age 5-10 children are fully competent users of the language for general purposes. And of course vocabulary learning (often associated with education, at least for some domains of vocabulary) continues all the way through adulthood. But vocabulary itself isn't generally considered part of "native speaker" knowledge.

So the answer might be that around age 5 some things become harder to learn, at least in some individuals. So starting to learn a language after 5 years of age means it would be harder to learn and you might not easily develop all of the native speaker competence that children learning the language do. I've met speakers who learned a language as late as about 14 years and are to my trained linguist ears completely competent and "native" speakers. But that might vary by what you mean as "native". And that's somewhat rare anyway. There have been a few adults (as many as 5% in some studies) reported to test like native speakers, but there are other studies that find that children who started learning a language as "late" as 3 years can actually be tested and shown to not be equivalent to "real" native speakers who started learning the language from birth (there are a few studies arguing for this perspective from researchers in Sweden who have tested Swedish-born speakers and children of immigrants who came to Sweden at around age 3).

A "simultaneous" bilingual, in the most prototypical sense, someone who learned two native languages from birth. So it's both native in the sense of "as a child", and also simultaneous in that they were both learned at the same time. Because of that, it seems to me that your age of 3 is about as old as would make sense: if you started learning a second language at or after age 3, you would be a sequential bilingual, not simultaneous. But you're definitely a simultaneous bilingual from what you said.

A sequential bilingual is someone who could be considered a native (or almost native) speaker of two languages, from early childhood. The most usual case is through school. So a child might speak Spanish at home and then learn English at school starting at age 3 or 5. A language learned AFTER 5 years of age might not really be considered a case of sequential bilingualism because it's getting beyond what would be considered a "native" language by some definitions.

So in your case I would say that you are a simultaneous bilingual (of which languages? ) and speak a third (English) fluently since childhood.

The technical term for complete fluency is nativelike. So you can say that you have nativelike English ability if most people think you speak it natively, or if, in general, there's no practical difference between you and a native speaker. Nativelike is fluent plus actually behaving like a native speaker. For example, you don't just have an ability with the language, but it's easy and natural for you. Being very strongly "nativelike" would actually mean you're almost becoming a native speaker. But by definition, adults (and maybe late childhood learners) can't become native speakers, so we use the term "nativelike".

But that's being very picky. I'd personally say it's fine to call yourself trilingual and a native speaker of three languages, with the first two being simultaneous and third being sequential. But that might not match technical definitions or cutoffs in formal research on these topics. Another area of complication is whether you show any signs of attrition (loss of ability) in the other two languages, and then questions of dominance. If you speak mostly English, are you still a fully competent native speaker of the other two? Do you feel comfortable in all domains? Is your formal education only in one (maybe English), so you don't know words for, for example, advanced mathematics, in the other languages? Does that actually matter? Again, it depends on definitions. But by most definitions you can't "lose" being a native speaker, even if you are no longer actively using (or have some attrition) in the other languages. It's complicated. And some people, at least for some kinds of linguistic research, would see monolingual native speakers as the ideal examples of native speakers. For example, if you're doing a psycholinguistic experiment measuring some kind of processing in the brain. Even if we consider bilinguals to be equal in linguistic ability, the other language(s) might interfere, so they might be excluded from the study.

An important point I've hinted at above is that actual ability and whether or not someone is "native" are not necessarily related. In fact, in some cases, they're completely different things. In the ideal/prototypical situation, a native speaker is a normal/perfect speaker, but there can be lots of variation from that for technical reasons and due to which definition you use.

Sorry for the possibly too long answer, but feel free to ask if you're wondering about any of those details.

On a practical level, I don't see why you can't call yourself trilingual with three mother tongues. But see my post above for some technical issues.

My question is, could this disturb the process of learning a language? Also, I have been having problems with English tenses since I started talking.

It could! It could also be interference from the other languages you know, and it could also be bad (non-standard) input from those around you-- maybe you learned exactly what you heard, but that just isn't "standard" English. So it depends on what the "target" was also. One additional problem might be that children tend to have some trouble with tenses as they learn them, so the interruption might have interrupted the natural process of correcting that. There's an interesting U-shaped curve that appears in learning inflectional morphology (as in tenses, plurals, etc.). First, children do it correctly (go/went, walk/walked, all memorized) because they memorize the input directly, then they start to do it incorrectly because they overgeneralize the rules they're figuring out (goed, walked), then they correct those overgeneralizations and reach adult levels (go/went, walk/walked, as adults do it).

There's work by Pinker and others I can look up about this, but just quickly googling "u-shaped verb morphology acquisition english" I get papers like this one:
http://people.cs.uchicago.edu/~dustin/papers/verb_morphology.pdf


More generally, a major problem and inconsistency in language acquisition research is the definition of "AoA", known as Age of Arrival, Age of Acquisition, or Age of Onset (AoO). Typically this refers to second language learners who arrive in a country (e.g., the USA for English) sometime during childhood or adulthood and then comparing all of those people to see how well they learned the language versus AoA. But AoA itself is tricky: what if they learned some English before "arriving"? Maybe "Age of Acquisition" is better, but what does that mean? Maybe age of first input? But why would a few words or your first sentence matter, compared to using it daily and getting full exposure? All of these things are problems. In general for research as long as the measurement is consistent for statistical purposes in an experiment it's probably mostly ok, but in your case you should think about when you started really using English (and the other languages) in a significant sense. Just a few words doesn't necessarily mean much. What matters more is the input and then any regular use.

It's hard to break habits. But the best option is just practice. Read a lot or listen to music. Then talk or write. A lot. You'll probably get there if you keep at it. Might take a while.

Of course for formal writing or to get a head start you could learn explicit rules but that won the much use in the average conversation in real time.

Not specifically, but like all linguistic acts, remembering will be easier in a language that is native or more natural for you. Thinking, dreaming, etc., tend to go along with fluency.

Two isn't a high number to assume a causal correlation (e.g. via a statistical test a sample size of two would essentially never be considered significant). And if there is some parallel cause then it could be many things. Cartoons might have unusual uses of tenses in some circumstances but I doubt it would be enough exposure ( vs all the other usage of English or even other input in those same cartoons) that you would be strongly affected by it.

There have been some studies that suggest language learning plateaus in adults, that it doesn't matter how much exposure you get, you just won't ever reach native levels as an adult. But of course there are many cases where people do learn, especially in limited domains with specific effort. But I really have no idea how long it would take in your specific case. I imagine if you make an effort to pay attention (this could be disruptive in your daily life!) and then correct yourself and keep practicing you will improve.

As for your current English usage, I haven't noticed any problems so I can't comment on improvement. You probably have more difficulty when speaking quickly, not in (relatively formal) writing, though.

Perfectionism is usually a limitation when learning or practicing a language. It's somewhat paradoxical: trying to speak well can limit how well you speak. Practicing, while not worrying about how well you are speaking, is usually best. Yes, you should sometimes pay attention to the details in order to fix them (to the degree they need to be fixed) but you should spend most of your time just practicing and making it all feel natural. More importantly, your perfectionist impression of your own speech will most likely not be similar how others perceive your speech. Even if your impression is accurate, it may not focus on the same aspects that are most salient to someone listening to you. In fact, one of the most difficult things to do with language (maybe almost impossible) would be to have the same impression of your own speech that others do. In short, it's complicated, and in addition to practice, self-awareness is good, but only in moderation. It's hard to comment further about the details without specifically analyzing your speech, but that's a general response.

As for books to read, you might find most valuable at this time some books about sociolinguistics or other topics about how to think about language in use. One that come's to mind is Anne Curzan's 2014 Fixing English: prescriptivism and language history. It's an accessible and uniquely balanced book that from the perspective of linguistics where we usually think of language in a descriptive sense (what do people say?), rather than a prescriptive sense (what should they say?), instead Curzan looks at some cases where prescriptivism have had an impact (and perhaps should) on English. So overall it provides an interesting perspective on what it means to be "correct" and so forth, and also addresses some myths like the idea of looking up a word in "the dictionary" (which literally doesn't exist!). Otherwise a more general book about language use in society (sociolinguistics, maybe even an intro textbook) would be relevant.

In the end, it's important to remember the relationship between language and identity. How you speak is part of who you are. There isn't exactly one way to do that correctly, but instead many options. "Perfectionism" only makes sense if you know exactly what identity you want to project to others and how to do that. Maybe some "errors" are in fact just part of your identity. Having an accent as an actor, for example, isn't necessarily a bad thing. Maybe the same for you?