Ah, OK... so, avast! isn't actually deleting anything, quite the opposite
As Technical said, those are warnings from the Behavior Blocker. avast! is warning you that
something (some other program) is trying to delete a file and it's asking you whether the operation should be permitted.
While it may be sort of suspicious for executable files, it's certainly quite a common thing today (in the second case, it's just Internet Explorer deleting the file (avast! Virus Cleaner) from its cache).
To turn off these warnings, just go to the resident protection control window, select the Standard Shield provider, switch to the 3rd page (Blocker) and uncheck those 4 checkboxes under "Blocked operations".