If you have any AV programs installed I suggest you run them. Response #4 may be an issue too.
I believe that when the flow of data drops below a certain point your ISP may think the line is inactive an drop you off for that reason. The spped could be slow because of the spyware you suspect you have. You could DLoad both Adaware and the latest updates to a different computer and transfer them via CD, flash drive, LAN, etc. Install and run without being connected to the net. Spybot S7D 1.4 is also very good. In my previous post I linked to a site that has both and more.