deadbolt won't turn

Misalignment of the shaft between door handles when in the fully inserted position and tightened up.

Yes

If it's a misalignment problem, then he can try not tightening the screws up all the way, leave it slightly loose and see if the problem goes away. If not, then the only thing left I see is that something is worn inside the lock mechanism and it's shot.

You door or the frame sagged and you need to relocate the striker plate.

Probably not. I can't turn the deadbolt when the door is wide open. Thus, it has nothing to do with the plate.

Probably not. When the lock was removed, I had no problem turning the deadbolt. So, the mechanism should be fine.

Usually this is because the plate sags when it is loose and when you tighten it up it binds. Try loosenening it up, see if it is better then if it is better, lift it up and let it down, trying to find the middle of that travel. Tighten it up there.

Those European latch systems have a reputation for beinf FUSSY. One of the 2 door and window companies I worked for years ago sold a lot of euro-style windows and doors - great product, but you needed to send your BEST installer if you were not going to have a come-back. They are made to be installed by CRAFSTMEN!!!!

I thought this the answer and rushed to the door trying to adjust screws only to find out that there was no screw to adjust.

A regular deadbolt has two sides, one for a key and the other for turning. This one has only one side for turning. There is no other side for a key. The other side of the door jamb has not opening. Obviously, this deadbolt is designed to be opened from inside only.

You still need to be sure the operating rod is centered in the hole in the lock. Move it up and down, side to side, then hold it in the middle of that range and tighten the screws.

I have seen a couple of apartments that have 3 locks on the door. A Knob lock, a deadbolt, and the third as you described. This would be a good thing when there are maintenance people who wait no more than half a second between knocking and coming in.

Three locks might be considered woefully inadequate in NYC.