I used to do organized centuries and I always stopped at all the rest stops. I always snack throughout the ride. If they provide lunch I hit that, too. I don't have an issue getting started again like some people seem to. If my legs stiffen it just takes a couple minutes to get going.
Also, I don't mind riding those things alone. If friends are there I will ride paceline with them but I am wary of strangers. Sometimes I will draft strangers but not often. If I do I try to check them out first. I would rather ride solo than get mixed in with a bunch of people I know nothing about.
If I get a muscle cramp I will just spin at low power. After a while they usually go away.
Above all, have fun. Chat with other riders, crack jokes, and enjoy the day. This part might be tough if you're riding a solo century.