Yessir. They're forms you fill out with your character's information. There are usually rules regarding limitations on characters. You'll either find these on the SU form itself or in the actual rules.
That really depends on the RP, to be honest. The game or the anime seem to be the standard setting, though the maturity of the manga is often integrated to some degree. (I've actually yet to see an actual Pokemon Special Adventures RP though.)
Adoption is simple. Well, at this point anyway. Getting adopted is the big step. As of now, I'll be watching over you and I'll be available to help you with whatever you need. How you treat the adoption is really up to you. I personally consider it a very... personal experience. That being said, I'm here for whatever you need be it answering questions, support (emotional, guidance, or otherwise).
Joining an RP is fairly easy. Within the Roleplay Corner there is a sub-board called the Roleplay Lounge. That's where all the Out Of Character threads lie. What you want to do is browse around, read the plots and rules of an RP to get an idea of what you're getting into, and then search for a Sign Up (or SU) to fill out. It's basically a character sheet.
Generally posting a Sign Up is enough to get you into an RP. (In some rare cases RPs do not have OOC threads and their IC threads contain this info.) Before you fill an SU out though, you want to check and make sure that the RP is actually accepting new members. Some are, some aren't. You can use the "Check to see if your roleplay has been accepted" thread to help find new roleplays, which are usually accepting new members. Some older RPs accept new members as well however, and may be less prone to dying off.