What type of damage could occur & what are the related cost repairs from reverse polarity, while jump-starting a car?

first battery gets a little cooking might survive, then alternator gets a reverse blast ov voltage against diodes, if short duration may be ok[ive done this many times till now i paint big + and- on battery,hopr radio was off [diodes] also a diode in hood fuse box and check the big 1 inch fuses they may have saved yo but

The thing to really check for is the computer I think it's called an ECU. If this was shorted you will have to replace that the good news there would be that salvage yards may be a resource to finding one cheap as well as ebay. Just make sure to talk to the dealer to find out exactly what computer number you need.