Did you purchase a complete replacement for mirror or just the pieces for the turn signal? I assumed that other than the turn signal, the complete mirror would be plug and play (for heat, power, bsm) into factory harness?
Minor scratches? You could try a good waxing and buff or maybe this?https://www.chemicalguys.com/vss-one-step-scratch-and-swirl-remover-compound-polish/vss-scratch-and-swirl-remover.html
Otherwise talk to a professional detailer?