In large part, the answer to your question is no. SOME of those things you could manage to do, but you're not going to really be able to do all of them. At least not on Windows without some ridiculously expensive software. On Linux it'd be absolutely no problem at all.
The closest thing you could get to what you want is to store data on a NAS device. Then both of you could access the data on this NAS device. This has a few problems with it, like only one of you could be working on the data at any given time, and it requires an active network connection at all times.
The thing to note here, is that Windows was designed at the height of the stand alone PC era. Every PC was an island unto itself. It's only been in later years that they've started bolting on any kind of networking features at all.
This sort of thing really just doesn't fit into that development model Microsoft is using. If it were Linux, you could transparently log into the other system, run programs, access documents, etc, and if set up right, never even know you were doing it. But Linux tries to emulate the system from the days of the dumb terminal. Of course before you go getting all excited about that, remember that Linux won't necessarily run your Windows programs.
You're pretty much screwed on this is the long and short of it. You can share data to a limited extent, but nothing quite on the order of what you want.
I have 1 desktop PC. Both my wife & I use it frequently enough so that we plan to buy a laptop so we can both work on them. Is there a way to use a file on either computer and make sure it is updated on both? For example: if I update our Quicken data on one PC, can that updated file be available on the second PC? If I add photos to MY PICTURE file on one computer, can those photos be seen on the second computer? If I receive email on one computer, can it be seen on the other computer? etc, etc, etc.
I'll add a possible problem: Our current PC is Windows XP. The new one will be Windows 7.
As always: thanks for taking the time to respond.