No they do not
No, the networks and games are not connected on the same servers.
The servers seem to struggle on the Xbox 360 and PS3. This may be because they are doing work on the servers, also hundreds of people may be playing at the same time. I can not bet on this but I think the servers will be better on the retailed game.
yes
No you can not because they are on two different servers and platforms.
The same amount as any online game would for the xbox 360.
by joining servers and on the menu of the game look for a part that says xbox live and its going to tell you join a match and you join
No, it was only said that some support will be discontinued. That means no more console production, new game releases, etc. As for servers, those will remain functional and viable much longer, especially considering Microsoft shut down the original Xbox live servers in 2010 - 5 years after the release of the 360. The 360 is much more common than the Xbox ever was, not to mention Xbox LIVE over the 360 and One is the same network, vs. the original LIVE which was independent from the 360's version.
No
On the Xbox 360
Firstly, because Xbox and PlayStation use different servers. Secondly, because PlayStation and Xbox do not have connected accounts, so it would be possible to have multiple people with the same name online. Thirdly, Xbox and PlayStation are directly in competition with each other, why would they work together?
Yes, in a way. Xbox Live is the name of the online service, and your Xbox Live account is the same across both consoles. This means you can log in on both an Xbox 360 and an Xbox One with the same profile, and your gamertag, friends list, and achievements will be shared.
when u play left 4 dead 2 online on computer it is powered by anti cheat servers so maybe it is the same for xbox 360