reversed polarity jumping battery

[George Lollar]

A few months back car would not start and while jumping reversed polarity briefly.  Car then drove home badly, missing and backfiring.  Battery replaced, car would not start, adjusted timing after which it runs well when cold but returns to same bad running when warms up.  Cold idle about 1100 rpm, was 650 before.  Coil and plugs are new.   Any recommendations appreciated.
Other damage - turn signal relay, fuel gauge not working (probably sender).   

[BobH]

Hello, was everything working and OK before this happened?

Hopefully you've just popped a fuse or two, the indicators and fuel gauge are both fed from fuse 5, so this may have blown.  I would check all fuses before you do anything else

Worse case maybe damage to the voltage regulator, but if the leads were only reversed for a second or two, you may have got away with it.  Measure the voltage at the battery with the engine running

Let us know what you find

[Cees Klumper]

Since it runs well cold - your warm running device may have gotten stuck.

[mdsalemi]

Just as an FYI, it may be helpful (to prevent something like this from happening again) to place those RED and BLACK felt things on top of the battery posts. Makes it quite clear which is which. On a modern car, it's very different. Mine has a massive plastic/rubber cover over the positive. Never any mistaking + for -. These are available at most auto parts stores and online too. They are generally made from chemically impregnated felt so they help to prevent that "white stuff" corrosion that shows up.

https://a.co/d/1GqEoWk

[Pawel66]

I am far from educated to figure out how reversing polarity might have affected engine running, assuming the blown fuses were replaced. We would need lPeterssen here...

But if I had suspicion that the current engine running is related to polarity reversal event, and if engine runs well cold and has issues running hot, and if you try to figure out how it might be related to electricity, I would then try work with electric components related to that. That would be relays responsible for switching on cold start valve and cold start solenoid. I would start the engine and then disconnect both of them.

If you have the FIP cold start solenoid in your car, I would check if it is not stuck in working position (remove it and hook it to voltage, see if it is working).

But I am shooting from the hip here...