I understand that in order to go for an obligatory hajj that I must have my debts paid off. Does this apply to mortgages and student loans, which include interest and will take a long time to pay off?
If you took the money with the intention of istinqadh (see Manual of Islamic Laws for more details) and not a loan then you would not be considered in debt and that amount of money taken (i.e., for mortgage) would be included in your assets. As a result, hajj would become obligatory if you become mustati or religiously meeting the financial criteria of being capable to perform it.