doorshinges
The door seems to tilt backwards which makes door closing hard and I'm thinking it's because of this old top hinge with the screw sort of exposed.
I'd heard that tightening the hinge could help but I have no idea how would I do this with this kind of hinge.
I also have no idea how would I replace the hinge.
Is it even possible ?
While Chris Cudmore is right about the real fix, you could work out a temporary fix as follows:
Brace the door
Rebuild the hinge holes
Reset the hinge screws
Quite a bit of fuss, but the only real cost is a few decent clamps. You need screw types, not spring clamps.
Or you could ask your landlord to fix /replace the door.
It looks like a lockring is used to hold the screw in place. You'll have to hold the screw still and rotate the lockring, or vise versa.
Using a flat-head screw driver and mallet, is a common way to rotate lockrings. Though, you'll have to find a way to hold the screw steady, while you bang the lockring free.
It's possible that the lockring is made of some type of softer metal, so grabbing it with pliers could easily damage it. Using a screwdriver and mallet applies force only in a useful direction, whereas pliers apply non-useful forces required for gripping. These non-useful forces may damage the lockring.
Best Answer
That is a pintle and gudgeon hinge. Usually the pintle is on the wall and the gudgeon is on the door, so that the gudgeon cup does not fill up with debris.
Search term "gudgeon", or "pintle", or "pintle and gudgeon hinge".
It is designed to come apart by lifting the door straight up. Then the individual parts (the "gudgeon" and the "pintle") can be unscrewed from their pilot holes.
In your case, you would remove the door, screw the top fitting further into the wall, and replace the door.
This will be complicated by whatever caused the fitting to start from the wall in the first place, which probably will require removing the fitting and repairing the hole.