1. It seems that they do.
2. If the answer for the first question is right, so the answer for this one is yes, as well.
3. Very hard to say. Possibly yes.
4. Don't know- in my opinion no, they don't set any flag, but some other bans lead to change mind...
----------
Time for my research results:
I used some IP resolver and IP logger (only for outgoing connections). I am very confused, I can't make any straight, sure conclusion. There were MANY, MANY, MANy outgoing connections to very unfamiliar IPs. I switched off every program which might cause movement in my network, but there's nothing sure about it at all. BUT I have few adresses, that may be interresting:
207.46.246.6- Mr. William and his friends in Redmond (WA)

Yeah, it's the main XBL server. The box seeks for it at every first connection.
Don't know why, I've connected to IANA organisation few times (maybe I'm laming in this subject, so just leave it

). IANA is Internet Assigned Numbers Authority. Dunno what is it.
Few connections to Korea, Netherlands and few other countries, but NO MORE connections to 207.46.246.6 or any other IP of this ISP. It might also be some spyware installed on my computer

.
So I actually dunno what to say... Only that there has to be something in these games o_O. Maybe if I had a second pc, and one more xbox I could figure out some logical relationship between those IPs and Xbox connected to the internet.
If you are cleverer than me and you think you can find something here, try to do it the same way as I did. It may be very useful for all of us.
I was risking my EEPROM, and I'll probably get banned very soon, but I think I can find 80$ for another Xbox... Or simply don't sell the present one, when my Kasumi blue box arrives

.
When you play this game once- it bans you. My friend who got banned 2 times in a row... got banned 3rd time. He flashed the EEPROM with NIC cable unplugged, turn the chip off and went on Live. He was playing for few hours, and the next day he got banned again. He didn't make to turn on the chip again when he got banned again. That's pretty sick. If M$ is not scanning the HDDs in search for game saves, it is scanning them at least for the serial number and bans the console again if the HDDs s/n matches to the last EEPROM. That's my new theory about recent bannings.
I also know one guy who hasn't played any of those games yet, he's using chip and blablabla. He has only Unreal Championship, Rainbow Six 3 and one more game. Anyway; he DID NOT get banned as almost all the other ones, who have used one of the "dangerous" games.
And especially for you, Artist: I know few ppl who are holding ALL their homebrew stuff on F partition and they've got banned. How about that? And games surely don't switch on your Xbox at night :/.
So... the one and only thing that everyone of us has got is actually the M$ dash.