I wish I could be of more help, but here are my "sort-of" answers.
A. Your parents should be able to name you on the deed even though you are not on the loan.
B. This is a question for a CPA. Realtors are not legally authorized to give this type of guidance.
C. This would be a good question for a real estate attorney (or probate attorney) or your parents' lender. Typically, being on the deed is different and separate than being on the loan.
Sorry I can't answer better than this. I do have some great resources I could set you up with for attorneys, lenders and CPA's if you would like. Just call me at 503-522-5803.