As I write this, I am using another computer than mine. This is Windows 7 running IE8 and protected not with Avast, but with Avira. To my surprise, IE is crashing frequently and, just like in my own computer, it does not necessarily close the window or tab; sometimes it does, sometimes it does not, but in both cases it frequently tells me that it has closed.

I will therefore stop speculating that something is wrong with Avast. It obviously is not.

… And here I consider the subject as settled (even though I have my problems still) and thank you for all your input.

Best,

J.P.