It is highly likely that the VGA port in your laptop is for adding a monitor to the laptop, not for using the laptop screen with an external device.

You need to use an actual standalone monitor, not the laptop screen.

have you bought a new xbox 360 since you bought the earlier games?

If so you may need to transfer the licenses for the games to the new xbox 360, you can do this from xbox.com

http://www.xbox.com/en-GB/Support/LicenseMigration/Home

mostly installing a game reduces loading times, but some games do have some improvements in other areas. For example I think installing Mass Effect reduced some of the issues with the graphics, so you may see a slight improvment.

It depends on the game, most games with co-op allow 2 player split screen, some allow 4 player with two on each console and others only allow one person per console.

one important thing: if you bought a new copy of Mass effect 2 then don't buy cerberus network from the marketplace

The best idea is to get it repaired. Since its RRoD you should be able to get it fixed by Microsoft for free. Go to the repair section of xbox.com

https://service.xbox.com/servicehome.aspx?mkt=en-gb&lc=2057

and fill in the details.

You find them through the game, usually as part of an extra mission

Yes, though you should check the backwards compatibility list http://en.wikipedia.org/wiki/List_of_Xbox_games_compatible_with_Xbox_360 because some games don't work / don't work well.

Generally for open NAT you need to go to your router configuration page on the PC and ensure that Universal Plug and Play (UPnP) is enabled.

With a bridged connection there may be other complicating factors, but try this first.

when team mates die in battle you can revive them with spells

they also come back when there are no enemies left after a battle.

There are merchants who will buy and sell items