1. It shouldn't be a problem if your version is out of date (unless very out of date, you don't mention what version you do have), the repair function should still work.
If that doesn't work try, uninstall, reboot, install, reboot.
It would probably be best to first download the latest version of avast
http://www.avast.com/eng/programs.html and save it to your HDD, somewhere you can find it again. Use that when you reinstall.
2. Can you give the exact error message ?
What were you trying to do when it failed to connect ?
What is your firewall ?