Sounds like you need a new latch mechanism.
Passat door lock problem.
The answer to 1 is yes you have a problem with the lock cylinder.
The battery is likely dead and needs to be replaced but the remote s may also need to be reprogrammed to work.
Maybe it is keyed different.
When where needed.
Common door locking module in this video i show how to deal with the problem buy a vw g.
If the unit is rotated anti clockwise then the door lock will be in the locked position.
The door lock works in only one direction.
If this happens the problem is with the remote.
The two parts metal and plastic are supposed to move as one unit.
This issue also indicates a bad lock actuator.
Locks work from the switch but not the remote.
As you can see in the photo on the lock actuator replacement part for my car door there is a plastic part left and a metal part right.
How gain entry via a vw door that won t open from inside or outside.
Raise support the vehicle safely according to manufacturer jacking supporting positions.
If you can get you remote working no big deal.