Randonneuring is a form of unsupported long distance riding. You can find a lot more about the rules at the
RUSA website, but basically, you must follow a specific route and are given cue sheets which tell you every turn to make on the route. Randonneuring is non-competitive, but you must complete the route within designated time limits. You stop at designated controls, which are usually convenience stores, and get your brevet card initialed to verify your completion of each leg of the route. If you like collecting hardware, there are awards given for lots of different accomplishments in randonneuring.
Yes, if you are riding 100+ miles a week, you should have no problem completing the distance. As for nutrition, everyone is different, but for many, becomes very important on long distance rides. Solid food takes enough hours to digest that it won't help much on a ride, nutrition-wise, but many of us need a little solid food to keep our stomachs settled. Maltodextrin based endurance drinks are a very good form of carbs for fuel. On the other hand, if you're one of those people who are able to fuel completely with fat, then water and electrolytes may be the only thing you need.
My recommendation is to drink plenty of water and endurance mix, add electrolytes if your endurance drink doesn't have them, and eat just a little solid food. But, you'll just have to experiment to find out what works best for you, and how hard an effort you put out will definitely make a difference on what nutrition you need and can keep down.