Does touching women temporarily forbidden in marriage nullify ablution?

It is prohibited to touch, or to shake hands with such women as they are considered strangers, and doing so nullifies ablution.

What is the ruling on istibra' and how is it performed?

Istibra' (cleansing from urine) is recommended. It is for a person to ensure that nothing remains of urine in its passage before performing istinja'. Its method is: to clear the throat (or cough slightly), shake the penis (meaning to pass fingers along it to expel any remaining urine if needed), and walk a few steps to the extent that one thinks nothing of urine remains if walking is needed. Each person knows his own nature best. The preferred opinion is that this differs among people. The objective is for one to think that nothing remains in the urinary passage that he fears will exit later. And Allah the Almighty knows best.

Which takes precedence: the 'aqīqah or the uḍḥiyyah?

Is it permissible for a mother to stop her daughter from marrying a respectable, God-fearing young man because he isn't college/university graduate?

It is impermissible to deny a woman her right in getting married except for a lawful reason, and problems can be solved through dialogue. However, she can file a suit in order for the judge to have a say in that regard.