Translation:I would only want him to try a little.
It refers to the area in which he needs to put some effort: grades, work, being friendly... because ci is a pronoun, you know that the area in this guy's life that needs work has already been mentioned earlier in the conversation. Ci and ne make these kinds of references more frequently than in English.
Well, he has a problem in a certain area that he needs to work on. (See the first two comments on this page.)
The problem with your suggestion is that in your sentence, the "it" refers to a possible solution that he should try: Try it, it might work. But in the original Italian sentence, the "ci" does not refer to something he might try, but rather to an area where he might try something. (Again, see the first two comments on this page.)
To repeat, not something he might try in a certain area, but rather a certain area where he might try something!
Given what I just said, I think "there" might work better than "it" here as a translation of "ci".
I don't think you need a lot of context to understand what is being said. For example, if I say in English, "Concerning that matter, you should try a little harder"' or "You should try a little harder there", you don't really need to know what the matter under discussion is. In order to understand the sentence, it is enough to know that there is some matter or other being alluded to.
Same for the Italian. You just need to understand that "ci" here is a general allusion to some topic or other.
Yes, part of the problem is that we are dealing with a computer program. But another part is that English does not have all the various subjunctives at its disposal that Italian does.
Here, for example, we have the imperfect subjunctive, "provasse", used because the main clause verb is in the conditional. How should we translate that verb into English?
I myself would choose "try" here rather than either "tries" or "tried". In other words, I would use the English present subjunctive rather than the present indicative or the past indicative. So, translating the Italian very literally: "I would like only that he try a little".
I, too, would use "try" [subjunctive], if I had to begin the sentence with "I would like ...," although that structure certainly sounds awkward. We would be more likely to say, "I would like him to try ..." The subjunctive in English is often used automatically, without the speaker realizing why the verb is not in a more common form. In addition, as in other languages, use of the subjunctive in English is increasingly uncommon.