Doe anyone know if I will damage anything if I remove the heat shield over the exhaust manifold and run it until I can find a new one?
The bottom bolt is broken inside the manifold, the top right bolt hole is broken on the shield leaving only one fastening point on the shield and it makes a terrible vibrating noise when the engine idles at lower speeds.

 

i dont do it personally and havnt heard anything about running with out them...but i have seen people that run with out them....

 

People have removed them without problems. Keep an eye on heat damage to your radiator fan & nearby plastic stuff. If you live in the Sahara where it's always really hot, then be especially careful... But it'll probably be OK.