When you want to use TK to attack a figure with an adjacent object token, do you have to have line of sight to the figure?

Yes

Yes. Also, if that character is within 10 squares.

10 squares away from the OBJECT, not the figure with TK.

You must be within 10 squares of the character you want to hit. You must be adjacent to the object. The object does not have to have a clear line of fire.

Your TK figure does have to have line of sight to the target of the attack. One thing to keep in mind, though, is that you do not count the object you are TKing when calculating line of sight. If a stealthed figure is only hidden by the object you want to attack with, then you are able to launch the object at them.