I can't answer all your questions but I can answer some.
There are several sites where you can play backgammon: partygammon (related to partypoker), play65.com, ... This link will shows a ton more:
http://www.bkgm.com/servers.html
Mind you, not on every site you can play for cash (I don't know about rakeback deals).
For practice you can either play humans or bots. Humans you can play for play money, ranking (f.e. on fibs = first internet backgammon server, most popular rating site), or for real cash.
There are several ways to learn the game, but if you want to get really good at it you will have to read some books and perhaps even more important, play the bots. There are 3 bots that are considered very strong: Snowie, Jellyfish and Gnub. Only gnub is completely free of charge. Snowie 4.0 is considered the strongest bot. These bots will increase your skill dramatically; no human has been able to beat them consistently as far as I know. Not only can you play these bots, they also allow you to analyse certain positions, to do rollouts, tell you how strong of a player you are, etc...
I don't know about any training sites for backgammon, but due to the bots (you don't have any pokerbots that consistently beat humans) it doesn't seem necessary.
The book I have heard most people advise for beginners is Backgammon by Paul Magriel. Another known authors is 2+2's own Bill Robertie.
Last thing I want to mention is that backgammon is not a game of partial information like poker. All the information is out there (which is why, I think, the bots are so strong). But, like poker, it also has a brilliant blend of skill and luck.