My parents have lived in the states for over a year and they decided to stay here permanently. Their green card is still pending,but EAD has been approved.
----Can they now buy a house in the US for them to live in?
sure, we bought our house when we are with H1, even no EAD. but they may have to pay a little higher interested if not greencard/citizen.
---Are they (over 65 years old) qualified for senior property tax exemptions?
yes, this have nothing with their immigrant status.
---Can I be the co-owner so that in the end we don't have to pay for the heritage tax? I currently own a house.
yes, you can co-owner.