No, solar panels will not compromise your roof, not any more than sitting on a chair will compromise the chair, even less in this example.
You will need a hole or entrance through the roof, so that is a compromise, but you already have a lot of holes for vents. The Fridge vent is a hole you can use if needed too.
The weight of a panel is nothing on a roof.
Did I read someone said a new tank is $1,000? No. Shop around. You could even find an RV in a junk yard with a perfectly good propane tank if needed, and pick it up for dollars.
If money is an issue then plumb in the bbq tank and use them, they are cheap and easy to come by. your brother-in-law will give you one just for feeling sorry for you.