>I am pretty sure now that the problem has to do with the specific Outlook.pst file. On this computer (where I am typing this message) I have the same Office 365 and Outlook installed. And when I would start Outlook (up until 1/2 hour ago) I never had a problem with memory leak.
>Then now that Avast completely f*cked up my "main" computer, I need to temporarily move files from "broken" computer to this one. I copied the Outlook.pst from the "broken" computer to this one and now when I open Outlook 365 on this computer and click on Reply to any message, the memory leak starts.

Rebuild the cdxes... :)

Really, sounds like some internal tables got whacked. See if that database (what's it internally, JET?) has an equivalent of pack command. Just rebuild it - or create an empty one and import everything from the bad one.