I never turn Free Will off, but I recall an incident from my very early game when Hans Moltke was still a toddler. He had used his potty, and his mum Manuela Moltke emptied it. She took the potty contents in a little black plastic bag, to the bathroom in order to empty them down the toilet. Unfortunately, when she got there, her teenage son Julian (who is now married to Andrew) was using the toilet. Manuela is perhaps not the most patient of women. When she saw Julian using the toilet she (rather unreasonably?) lost her temper with him, and threw the bag of pee and poo on the floor. Whereupon it turned into a pile of rubbish / trash. Fortunately there was no cockroach infection or 'flu outbreak, because Julian (with a calmer temperament than his mum) took the rubbish outside to the dustbin as soon as he'd finished on the toilet. (No wonder I sometimes think that teens have more sense than adults!)

This really is ancient history in my game: Hans grew up from a toddler to a child on 1st February 2013! I've just been looking at his birthday party photos.

Is it possible to find out the college professors' associated majors without noting down the notifications when the students first meet them?

Yes, if you have SimPE. Whatever their University Major was, will be the subject they teach.

Can elders adopt? I've read that they CAN, but in my game they can't.

I've had them adopt. However, now this is just a guess, but maybe it's like an adult havin kids and there is a stopper if they're X days from dyin. We can't see how long they have left in game, but you can check in SimPE and see.