What you need to look at is the mod document, what value are they using for the baseline. When they got this mod a lot of homes were underwater, so did the mortgage company place a new value on their house at say 400k? so any amount over 400k they get 25%, or did they keep the original value of the house at the time of the 2004 mortgage which would be say 525k. That is going to make a HUGE difference in the amount of the money they get to take home.
if the mod was from 2011, you most likely won't have a prepayment penalty. They are usually anywhere from 1 to 5 years, but to be sure, that will be in the mod doc as well.
And at this point, you don't need an appraisal to know what their house is worth, just figure out on your own, what did the surrounding homes on Zillow sell for in the last 6 months. If you are really struggling on this, just get two or three local relators to swing by they will give you a very close number for what its worth. I am curious to know if the servicing company uses the appraisal or is there some language that states they will use what the house actually sells for.
Payoff day is the day they pay it off, like in 3 weeks. You don't need this much detail in estimating your payoff amount. If the loan is current, just take their remaining principal balance and add 75% of one payment to it, that's a pretty good ballpark.