My son has a 1995 Chevrolet Cavalier (2 door).
Currently he has 4 * P195/70R14 All Season Radials on this car.
The tread on these tires is quite low.

A neighbour used to own a Cavalier (not the same model/year).
He has 4 tires on rims with really good tread.
They are BF Goodrich P195/65R15 89S mud and snow (Touring T/A SR4).
Is it OK to use these rims and tires?
Are there any potential issues?
If these are OK, I assume that they would not have to be rebalanced.

Thank you very much in advance for the advice.

should be ok, just make sure the bolt pattern is the same and check for slight clearance issues.