The standard recommendation for towel bar height is 48 from the floor to the center of the bar i tend to hang mine between 44 48 high.
Bathroom door height off floor.
The standard i use is 1 2 over finish floors 3 4 is acceptable.
That is a lot of room for unlevel you have there.
The additional room allows for a 3 4 inch top jamb a shim.
Interior door height off floor.
I just took a quick look at some of standards and regulations governing door undercut which is the distance between a door and finished floor as opposed to clearance which is door to sub floor.
The ceiling in your bathroom must be at least 80 inches at the front of the sink or toilet and inside the shower.
The awi gives no minimum but a maximum of over 3 4 is unacceptable.
The height of common doors is 6 feet 8 inches.
The front of the toilet needs to have at least 21 inches of clearance.
Place the door handle at about 900 millimetres off the floor or wherever is comfortable for.
The shower door needs to have an opening clearance of at least 24 inches.
I prefer to run shower enclosure glass to the full ceiling height with the door just slightly below to allow for a free swing as i did in the bathroom shown here.
At the back of the sink or toilet the ceiling height can be as low as 60 inches.
To fix the issue the doors need to be removed bottom of the jambs cut and reset the door.
A 450 millimetre wide fixed panel and a 600 millimetre wide door panel work well for a typical 1500 millimetre tub.
I have never seen a door set with that big of a gap unless it was to get past floors that were not level.
When determining the best towel bar height for your space you need to take into consideration how your bathroom is laid out sometimes the placement of outlets and light switches can affect things.
So says the building code.