No,that has nothing to do with Kazaa. Mails are totaly seperate stuff which comes from a remote server,so you don’t have anything on your disk (as you already noticed after doing boot-time scans).

Timeout is a time in which remote mail server doesn’t respond. Try increasing Timeout number in avast! mail scanning provider.

Possible Infection detected warning is a heuristic part of avast!.
Examin marked messages with care and don’t launch attachements in such mails.

So most of the mails you got were infected and can be deleted or added to spam list (if you mail client supports such feature).
If you add these infected messages to spam list you won’t have to sort them later.