Sure, although it's a loose set of definitions.
A group build is (generally) a member-initiated effort to have a group of modelers tackle a certain theme. Recently FSM has started hosting them, but even there Tim and Aaron really act like any of the rest of us.
It all depends on a dedicated host. Good hosts spend a great deal of time answering questions and doing housekeeping.
You should look at some, and start with the initial post, read the rules and read on from there.
Badges are up to the host. Some GB's let you take one right away; others when you finish them. I don't post badges so I don't follow that too closely, but it's usually explained pretty well.
I personally dont usually join a GB and buy a kit, rather I look through whats up in GB's first and go check the stash. Its a good way to move out stuff.
Highly recommended and you can learn a lot.