1. You don't have to use compatibily mode. Make a shortcut to JJ2+ and add the command line parameter -menu after it. I can post picture of this if you need one.
2. This probably is a server-side problem. You can't fix it.
3. JJ2+ mostly affects multiplayer, but for instance pits work in singleplayer too.
4. Yes. Try searching 'bash' on J2O and download tilesets. Levels are probably outdated in Bash packs, so you have to download them through JJ2.
5. Hopefully.

Edit: NINJAS