Hello, my name is ***** ***** I am an attorney. I am happy to assist.
Usually we only answer one question per posting, but I will go ahead as a courtesy and answer all your questions.
The easiest way to accomplish this transaction is to do a Quit Claim Deed from her father to the both of you. That provides no guarantees as to title, but is the quickest and easiest. That is then filed with the registry of deeds to make the transfer legal.
The deed can't be filed until you resolve the existing mortgage on the property. Sometimes large banks will allow a mortgagee to assign the loan to a family member, so that is an option that could make it easy. You could also add on a home equity line of credit while you do that assignment, to give you some funds for improvements.
If the bank won't allow the assignment, then you just need to apply for your own mortgage and your bank will pay off the bank of his mortgage at the closing. You could also just pay it off in cash if you prefer, but you can't deduct any of the interest payments, only he can, so I don't advise that.
There will be taxes on the transfer, based on the increase in value, and you do still have to pay that, even if he gives it as a gift. This question is best suited for an accountant, but I believe there is also a way for the father to take on the tax implications instead of the two of you, if that is what he is willing to do.
Property taxes always have to be paid, so if there are any outstanding taxes you would be responsible for those once you purchase the home.
Legal fees vary, but generally a closing is around $1,500 and then there are closing costs that can range from $500 to $2,000 or so. All that depends on the location, lawyer, bank, etc.
Let me know if I got to everything, and if you have any questions about the above.