There is one behavior I can't quite figure out, but I think I have an idea. When I did a hard reset, and I sync my phone via USB to my pc, some 3rd party apps gets installed automatically without me doing a thing. I think it only installs the apps that I've purchased through the Zune software on the PC. Zune seems to resync more than just songs, movies and pics, it also resyncs your apps.
I would test it to verify it, but I don't really feel like doing another hard reset :D
Yes apparently if you download through Zune, then you have the apps available in a list onzune, but not ones that you download straight to the phone you can't track. I am trying to keep it updated on OneNote.
Yes, a little playing around found this answer out for me as well...but this process should be more sync'd and consistent between Zune Marketplace on PC and on phone, especially if you are logged into both with the same account. Hopefully, this will be addressed in one of the upcoming updates (along with a better search function :P).