Hi Mich and welcome. I've moved this discussion to the Acquisition forum.

Online = internet? Or online = real-time testing? (In testing, that can mean two things.)

What kind of testing will you do? Will it be only reading text? Will it be writing? Listening comprehension? Proficiency is generally best measured in the domain that you are testing, unless you either don't need very accurate results (like just "high" vs. "low" learners) or you want to compare modalities.

There are lots of tests, but it's hard to recommend just one, simply because there are so many. One strategy is to look at previous research that is similar to yours and then use the same material they do (you can email authors and often they are very helpful!) or something similar.

If you are interested in just written language, then I personally like cloze tests or C-tests. A cloze test is basically a fill in the blank paragraph (or some sentences). Sometimes there are multiple choice answers, but often not.

A C-test is similar but you supply PART of the word so the learner must complete the sentence. For example, "Hello, h-- are you" -- the answer is "how", of course. This style of test is good for both grammatical (via suffixes, though limited in English) and lexical knowledge. And there is usually only one right answer. In a normal cloze test you can get several answers sometimes.

I don't personally, no. But for that type of experiment, I would think that a fairly normal written test, probably multiple choice (if you don't want to score the results later by hand), would work well. Look for some research on English cloze tests as one possibility. It would also be good to consult someone who specifically works in this area, because measuring proficiency is challenging (even deciding what "proficiency" means!).

You should also decide whether you want to have groups (like "high" vs "low") or a continuous value (like a score from 1 to 50). This will determine the kind of statistics you'll be using and will help to determine exactly how you will operationalize your hypothesis. Additionally, if you know that all you need is to split your subjects into groups, the specific accuracy is probably not as important. If it's on a scale then you'll want to be a little more careful.

Again, where I would start is looking at similar research papers to see what they did and if needed send some emails.