I'm kind of surprised by the 3-month thing. Are all your questions supposed to be answered to your satisfaction by then??? That's nuts. (I guess they are afraid Armageddon will come in 4 months, and you are not properly ready!) People learn all their lives long, and experience and insights keep us adjusting and fine-tuning all the time. You might consider telling them that you DO want to research everything out, to make sure of everything (that's in the Bible, so they should not be upset for your wanting to do this), but this is going to take a bit longer than 3 months. In fact, it will simply take as long as it takes--however long that may be.
Whether you accept a Bible study or not (see if you can at least push it off for a while, if nothing else), try to explain that until you can test it all out to your satisfaction, it would be wrong of you to be baptised or expected to talk with a conviction you do not have. It would be wrong of others to pressure you to commit to what you shouldn't.
You are perfectly right about faith being what everything all boils down to. Your parents seem to think that faith is something that is inferior to knowledge, which is why they push for you to "know" instead of recognizing the great role of faith. Faith calls for an element of humility; knowledge tends to puff people with pride. I think this is another area where they will not listen to you--simply because of what they already "know"--so explain that you understand their view... but can't yet agree with it quite yet.
It takes time to sort thru all the stuff. Keep your integrity, ask God to help you, and I assure you that over time, things will become clearer in a certain direction (and not simply bounce back and forth).
bebu