the copper crew card says you suffer 1* unless you flip up one of your damage cards. Can you choose witch one you flip up? Are you even allowed to look at the face down ones? Thanks

Per rules reference, flipping cards face up is random unless specified otherwise (c.f. Thane Kyrell). Randomize however you want.

No you can not look at face down damage card. The only time you can is once the ship is blown up.