edit: Add to the title, "during the age of exploration" , sometime between the 15th and 17th centuries.
Henry Hudson comes to mind when I think of this situation, but I know there have been other mutinies as well.
You absolutely do NOT sail back to your homeland. Mutiny, no matter what the circumstances, was a hanging offense. The navy was a pretty awful life, the only way to keep sailors in line was through iron discipline.
No, you don't do this either. All it would take would be one member of your crew to be drunk somewhere and blab. Additionally, there would probably be members of the crew who were against the mutiny. They would almost certainly talk.
Yes, immediately. You get tried for mutiny and summarily executed. Mutiny was treated extremely harshly.
Nope, because you've been hanged.
Sure, why not? Many sailors were borderline illiterate though. So you would have to find one who could read and write though, to do the daily log.
Nope. Again, you got hanged.
Nope, because you didn't sail home because you would get hanged.
Possibly? I mean, again, you didn't sail home.
You do! The point of the mutiny is that you get to be in control of the boat.
A lot of your questions required a 'yes' to your first question, so I'll give you a broad strokes response to what you would do if you mutinied.
So you mutinied and marooned the captain and probably the rest of those who were against the mutiny. What do you do?
Firstly, you probably get blind, stinking drunk. Sailors are notorious in their drinking habits for a reason, and in the undisciplined aftermath of a mutiny the rum stores would almost certainly be broken open.
Secondly, you would sail to an island with natives who were willing to trade/barter with you. You would stay there for as long as you liked. Compared to service in the navy, living on a tropical island with tons of fresh food, women, and good weather would seem ideal.
So, the end result is you living on an awesome tropical paradise, having sex with exotic women, getting drunk, and eating fresh fruit and boar until the navy came to pick you up and hang you.
Source: Captain Bligh's Portable Nightmare