As long as you aren't using a beverage package to buy drinks, you can put both of your drinks on either card. Since you have the HIA package, you must each put your drinks on your own card. No sharing.
No. On cruises years ago I was able to plug our wireless headset transmitter into headphone jacks on the back of the TVs in the cabins, with difficulty. Now they are mounted so tight to the wall that you can't get to them, even if they are still there. They are never on the sides of the TV. In my experience in hotels, more recent TVs don't even have a headphone jack, although they do have a digital audio (fiber optic) outlet plug.
In general, those tables can be moved, although we have had cabins in which the "coffee table" was affixed to the floor, er, deck.