If granted TDIU, will I still pay house taxes?
Maybe. Maybe not. That's up to the state you're in. Some states will allow a 100% P & T veteran to skip paying taxes on the mortgage (and auto registration and a lot more) and other states aren't quite as generous but there are still significant benefits.
To learn what your state can do for you, use the Google search engine to look for your state veterans affairs department and you'll find all that info in there. Good luck!