To answer in shorter form :
1 & 1.5) yes it's that easy, and yes RF tvs are ancient, you will need a cable or run it through a VCR that has RCA inputs.
2 & 3 ) you can go online with XBConnect; it's a peer-based and non-MS affiliated connection. No downloads from MS.. sorry. You can tell if an MS game will work with it; look for the "system Link" option for multiplayer.
4) Solo games are great; I like the fact that the Live service does help you even when playing solo. Live-aware titles (letting you log into the network but still be "offline" playing solo) means that you can play solo games and still be there to recieve invites for other online games.
Live can be linked to your MSN Messenger as well, so while you're fartin' around on the net you can see notifications such as :
12/2/2004 9:49:44 PM GMT-UTC
jeffjones66 is playing Prince of Persia: The Sands of.
12/2/2004 9:35:51 PM GMT-UTC
G4M3 0V3R is playing Counter-Strike.
So if I was waiting for jeffjones to play Halo2, I'd know he's online right now (playing a single player game such as Prince of Persia). (I'm -6hrs GMT, so it's 3:49pm or about 10 minutes earlier than this post). Live has some sweet stuff going for it; and I'm a PC gamer.
For reference, I was a hardcore PC player up until about 3-4 years ago; I used to host 30+ person langames on 100Mb back when the 16port switches were upwards of 500US. Hell, I started langames back on Arpnet with Duke3d.
The 16 port switch collects dust now.