Q: How is it possible that avast! finds viruses' in it's own folder C:\Program Files\Alwil Software\Avast4\Data\Moved? Does it mean that avast! is infected?

A: No, the folder C:\PROGRAM FILES\ALWIL SOFTWARE\AVAST4\DATA\MOVED is the default folder for moved infected files. If you find some viruses in that folder, it means that these files were found infected previously, and you selected to MOVE them - and avast! moved them to the mentioned folder (and changed their extensions to *.vir, so that you couldn't activate them by mistake).