From the Pandemic Rules:
The Dispatcher may move other player’s pawns on his turn (using any of the available Basic actions) as if they were his own pawn. He may also spend an action to move a pawn to any city that contains another pawn. He may only move other players’ pawns if they permit him to do so.
Note: For the Charter Flight action, the Dispatcher must play the card corresponding to the current location of the pawn he wishes to move.
If the Dispatcher wants to move ie. Medic's pawn, does he need approval of the owner or can he do it against Medic's will?
No, he can only move pawns if they permit him.
When making a flight with another pawn, does Dispatcher use his cards or the player who's pawn is flying?
Uses his cards.
Can the Dispatcher move his pawn to the city with another pawn or does this only apply to moving other pawns?
He may move any pawn to any city that contains another pawn, so he can move himself to where another pawn is.