if you want to install the game to the HDD, you need to do this from the xbox dashboard. go into game library, navigate to black ops one of the options should be install game.
as for game invites if someone sends you one you should see it pop up top right corner. then click the xbox button, and you should have new message there, accept game invite and you should join that game then. if you want to invite, you need to be in player match lobby press Y and select friend you want to invite to game