2. How do I now get Avast re-installed on this system without needing to pay for it again since it was so recently installed?
It is the license key you pay for......not the download of the program....you still have the mail with the license key ?

you can download again, every day if you want http://www.avast.com/en-eu/free-antivirus-download

but before i did, i would have essexboy check it for malware first

follow this guide and attach all logs…not copy and paste
http://forum.avast.com/index.php?topic=53253.0