You actually have several different questions here -
(1) Is a non-grounded 3 prong plug (in your specific building) legal according to local building/safety codes? (yes or no question)
(2) If the above answer is "Yes" does that violate local Landlord/Tenant Laws (also yes or no question)
(3) If the answer to 2 is "Yes" then you have to look at what your options are.
Here one possible resolution to talk with your dad about -
Let's say that Q1 is true. Now what? You report to the Building Code Enforecment. They find a violation, "red tag" your apartment and you will have to leave immediatly and stay out until the landlord fixes it.
The landlord at that point has several options - most of which involve you moving - as he does not have to fix it, he only has to fix it IF he is renting it out. He could sell the building, change it to condos, or lots of other options. He may also be able to just remove that outlet (assuming it's only one).
So much depends on your local laws - you have to find out the answers to Q1 & Q2 before you do anything.