A balcony door going out to the backyard has a mezuza placed on the right of walking into the house or on the right of entering the balcony?

Minhag Yerushalayim is to place it on the side which is to the right when you are going out. There are poskim to rely on either way. Better to be yotzei the bracha on a different mezuza, then put this one.

What if there is no post, only the insertion for the sliding doors?

You can have a professional make a cavity in the aluminum if that isn’t possible, people stick it on the face panel.

What if a room is 4 by 2 amos, does it require a mezuza?

No.

Are you aware of any such halacha that a married person should not have mezuzot that have a see through casing?

No. Plus the bedroom door usually opens in and when door is closed the mezuza is out of the room anyway