Have you checked connections on both ends of the positive cable and looked to see if there is any corrosion backing up into the stranded wires? You can try and replace the cable and see what it does. I don't think you would have fried the diodes in the alternator since they are made to deal with 12v normally. Not sure about the other electronics, but at this point, the quickest test would be to replace the cable and go from there. If it starts up, test voltage at the battery with the engine running. Then shut it down, volatage should be higher with running. You can also do some checking by turning on electrical accessories and see if the alternator compensates for the higher voltage drop.
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97 S90 with 180K miles still going strong

It sounds as though you have a battery cable problem at the positive terminal: if it gets hot, you've clearly got resistance at the cable, which can prevent a start and mimic a dead battery.

As for the reversed polarity, I think you are OK if you did not start the car. The initial sparking when you connected the terminals incorrectly was likely due to lamps and low-grade current supply. If you tried to start the car, I have no idea what reversed polarity would do to the ECUs and other digital electronics. I also doubt that it affected the alternator diodes, but even if these were fried, you could replace the regulator for only $50 or so.