Teacher's retirement can be a different thing, since teachers can opt out of the SS system. They may not have any credits unless they work a job before or after teaching. States handle this in different ways. For example, some states have a formula based on the amounts of money available from the retirement plans, then adjust the pensions accordingly.
This is a better question for SSA than a caregiver group, since it can be complicated. Some states may allow both teacher's pension and full spousal SS. I don't know.
Your mom does not get SS credits for time off raising a family. There have been rumors of legislation that would do that, but no actual passage. She should get some of your father's SS or all of her own SS, whichever is higher, but not both.
From what I understand, this varies by state. Your mother may be able to receive some additional money from your father's SS. It is best to check with your local SS office to find out and apply for potential benefits.
This is a better question for SSA than a caregiver group, since it can be complicated. Some states may allow both teacher's pension and full spousal SS. I don't know.
She should get some of your father's SS or all of her own SS, whichever is higher, but not both.