As a general rule of needing to pay 20% of our savings or money, what is the ruling if we live with our parents and they are having a house laon which they are paying and still owing money for. Would we be able to pay that 20% towards the house loan?

If your parents are owning the house, and paying the instalments, and the annual savings of each of them is lower than his portion of loan, then they do not have to pay khoms.
For you, you are not exempted.