Discussed this in class today (for Quechua):
1. It's fine to have an adverb and a direct object in the same sentence.
2. -ta is the regular suffix for forming adverbs from adjectives. There are other ways to form adverbs, but this is the main way from adjectives. And it may not work on every adjective, but it works on most (so it's productive).
3. It's fine to use these adverbs with intransitive verbs. (Note that in Quechua there's no zero-derivation between classes, transitivity, etc.-- "walk" is intransitive and to "walk a dog" you would need to add a causative suffix, etc.)
4. It's "basically the same as English -ly", according to my teacher.
Another example is:
sumaq-ta
good-ACC
'well'
This hints at an origin in phrases like "do good [things]" resulting in an eventual adverbial meaning.
So my guess, and just a guess, is that this usage started out in ambiguous contexts:
I do a lot = anchata
I do good (things) = sumaqta
Are those objects? Adverbs?
Then after these started to be used idiomatically, by analogy the suffix was generalized. This isn't so unlike English -ly, which was a suffix used to form some adjectives, eventually used as adverbs in some cases, then generalized and systematized.
There is an interesting implication here that adverb suffixes are somehow inflectional, rather than derivational. I've always thought that. There are some arguments out there against that for English -ly, but overall I think it's a better analysis than thinking it's mostly derivational. And here's another hint.
(More reasonably, there is no perfect distinction, and this is an example of a suffix somewhere in the middle, though I'd say mostly inflectional.)