1. going 5.1 can be done with bookshelf or floor standing, so not sure what that means. You don't seem to have a particularly large space, so imagine smaller might be preferred?
2. will be speaker dependent, there are some very good bookshelves and some poor floor standers....if the sub is sufficient and the room isn't too large then bookshelves should work just fine, tho.
3. you will need a full set of pre-outs on an avr to use active speakers, or use a pre-pro (generally pre-pros are more expensive than avrs, tho). Full set of pre-outs tends to only come on the higher priced avrs, too.
Is the $800 budget for everything or just speakers/sub? You had some decent gear, that's a pretty limited budget to replace it all with (or you could perhaps consider used). Holding out not so much, but maybe just starting with a simpler system until you can afford more....