Is a 100A breaker adequate for a garage subpanel?
Well, you asked several questions and if you search on this site you will find many questions and answers regarding sub-panels. We have covered this same subject many times. It may be the most asked questions from novices.

It would be a Code violation, and safety issue, to protect #6 wire with a 100 amp breaker. You will need #3 copper or #1 aluminum if you want to protect it with a 100 amp breaker. You can use whatever size panel you want at the garage but if you want to fully utilize it you should feed it with proper sized wire and protect that with a properly sized breaker.

You can drive the ground rod with a fence post driver they sell at the farm centers. If you have good soil they are easy to drive.

The #6 grounding electrode conductor connects to the ground bus and the neutral bus is kept isolated. Take the green screw (or the jumper strap) that came with your panel and throw it away.

Good luck and stay safe!