I think pravi is more like the state of being true, as opposed to false, while gxusti is more akin to being proper, sort of like being the right one as opposed to the wrong one.

As a side note, I've been trying to work out the difference between korekta and gxusta. I think korekta and gxusta can be used interchangably, but the impression I've gotten is that the connotation is slightly different. What I think is that gxusta is closer to the English "proper", meaning there are choices and this is the best, whereas korekta is closer to the English "correct", meaning there is one perfect answer and this is it.

In this particular sentence, the adverb placement is irrelevant because it is apparent what is modifying; however, sometimes placement changes meaning. Read this: http://donh.best.vwh.net/Esperanto/Notes/note03.html

Generally speaking, even though Esperanto word order is pretty free, modifiers precede what they modify, though that's not quite a hard and fast rule. Thus adjectives generally come before the noun they modify and adverbs come before the adjective or verb they modify.

I would say not really, as the root rajt- refers to what is allowed, what is legitimate. It's not really about the correctness of the response, but just about the fact that one was allowed to give a response to begin with, according to rules, customs, mores, or laws.