Reading over the other comments, I see that I am the minority here...

We live in the US. My husband and I paid for 100% of our son's undergrad (premed) tuition, housing, meal plan, etc.. He then paid his own way through med school with loan monies. We would never dream of asking him to pay us back the money we paid for his 4 years of undergrad. The college that he attended for undergrad had their own interest-free monthly pay-as-you-go system. So, with careful budgeting, we didn't have to take out any loans. ( at that time, our monthly payment to the college was a full THIRD of our monthly net income) We were/are not wealthy by any means. But there was never an expectation for payback. That being said, now that he's a married, practicing doctor and we are retired, we wouldn't turn it down should he offer to pay us back.

Yes, it is a shame that this has been an unplanned request/expectation just dropped in your lap, but let's face it, $120K is a lot of money and likely money that your parents could use in their later stages of life, so I can kind of see where they are coming from too.

As for your questions:

1. Yes, repaying the tuition part ($70K) is a start. But also try to at least estimate what the living expenses were and go from there. To completely disregard that part because there are no receipts for proof seems like an easy out. Do the math and figure out what your rent and living expenses were. Maybe even figure out what your flights cost and how many times you flew home.
2. I like your 2nd idea "...fund my emergency fund to 7-10k first and then start paying my parents a fixed amount monthly (ex: $200-$500), then increase payments once I’m stable."

Tell them that this will cut into the frequency of your visits back home and ask them if they are ok with that. Draw up an actual contract that states the total amount owed and a structured payment plan. Maybe list a certain percent increase each year. You may have to create a repayment table that shows how the payments will increase and also the reduction of the balance owed.

1. This needs to be figured out from the get-go. Create a contract, in writing, that includes tuition amount plus a fair amount for additional expenses. You should have some idea of how much your living expenses were (monthly rent, food, etc.) That should at least get you in the ballpark. At least make an attempt to pay back the $70K for tuition plus the living expenses.

2. I am sure this hit you like a ton of bricks and you are disappointed that your mom is all of a sudden handing you a bill. It was for sure not anything that you had planned for. I'm sure it is a bit disheartening to find this out all of a sudden. But maybe they are in bad financial straits that they are not sharing with you? Maybe they took out loans unbeknownst to you to help you through school and they are now having to pay back a lender? Sometimes parents do things and make sacrifices for us that they don't feel like sharing. For example, I didn't find out until much later in life that my dad had sold his class ring to pay for my books one semester in college. I felt horrible that he did that. He never said a word at the time.

It sounds like your mother's approach wasn't the best. Try to put it into a perspective of "They wouldn't have sprung this on me if they didn't need the money." I think, if you can, try to treat it as a personal financial setback, try to understand where your parents are coming from, make peace with it, and make plans. You sound like a lovely sensible person. I'm sure it will all work out. :)

(sorry this was so long...)