Although you cannot play story-mode missions online or in multiplayer, you can play other things, such as Death Match, or other multiplayer-based missions while connected online. You cannot, however, play 2-player co-op on the same console with two controllers.
No
that all depends on what GTA it is, GTA VC - IV it will mark a person on the map, if you go there the mission will start, older than that i cant help sorry
I believe this is Mission Number 51.
after the first mission with playboy x
You get nikos phone when you start the first mission
depends what mission you are on now
there is no real point to them other than playboys 'photoshoot' mission and a random mission you can do with Jeff
30 look on love meet after out the closet mission
Yes, there is a mission in GTA IV where you rob a bank. It is called Three Leaf Clover. You need a nice suit. You get the mission from Packie
Yes, Gay Tony does appear with Luis in GTA IV. They negotiate a hostage deal with Niko and Packie in the mission "Diamonds Are A Girl's Best Friend". Luis is also seen briefly in the bank heist mission "Three Leaf Clover" and "Museum Piece".
If you are playing GTA San Andreas or GTA IV games, it might be worth doing a side mission in the game, to see if this gets things started again.
There are 94 missions on GTA IV. For a complete list of these missions look in the related links section.