If you connect a set of jump leads the wrong way, you're likely to see a pretty big spark as you connect the last one - even if the battery you're jumping to is completely dead, the alternator's diode pack can carry a couple of hundred amps. If there's a fusible link for the alternator that will fail pretty quickly.
Most likely, the car won't even crank, let alone run with the jump leads connected backwards, so if it did so it would indicate that it was connected correctly. With older direct drive starter motors that usually had a wound field, these will run the correct direction even if connected backwards, and a points based ignition system will still generate a spark, so that it would maybe start, this would be true of many cars from the '60s or earlier. Newer cars with permanent magnet field gear-reduced starter motors will not turn the engine if reverse connected. Anything with electronic ignition will not start. By design, the electronics are supposed to be able to tolerate both reverse connection and load dump (more on that later).
The alternator has by design a limited maximum current, it won't run at that point for more than probably 10 minutes without getting excessively hot, but it'll tolerate a couple of minutes charging two batteries in parallel.
On disconnecting the jumper cables, if the alternator on the running car can produce a spike if the jumped battery is still very dead and has a high internal resistance. This is known as a load dump, and many alternators now have protection built in in the form of Zener diodes in the bridge, or an additional suppressor on the positive terminal.