It is likely that your daughter has a better credit score than your future son-in-law and that would cause the bank to offer better terms on the rate.
It is always a good idea to get the best fixed rate possible. If he isn't able to qualify for the best available fixed rate (I would not, under any circumstances, take out any form of variable rate loan at this point in time, no matter what the loan officer is promising) on his own then it is highly likely that the mortgage that he is looking to take out is more than they should be borrowing. If a payment is unaffordable ("affordable" is usually defined as being no more than 30% of your monthly gross income; depends who you talk to) using the best 30 year fixed rate that he qualifies for, then the loan is too large and they need to look at a smaller house. The single biggest financial mistake young couples make these days is buying too much house, under the assumption that they're income will grow into the payment or that they'll be able to refi to a fixed rate loan at a later date when they can afford the payment better.
No, they would not be able to file taxes together unless they were married. If they were both listed on the loan, then either one of them would be able to claim the mortgage interest as a deduction on their federal return, but not both of them.