1. I found "
Learn Lua in 15 Minutes" a while ago. It provides a very good overview of the syntax, as well as some additional links at the end.
2.
Wowpedia is probably the best resource for WoW API docs. I use it extensively when I don't know how to do something with the API.
3. Libraries are by no means required or even needed, though they do make certain things easier. Wowpedia has
a simple example of how to do Saved Vars without a library.
Edit: and Seerah's link too, good stuff.