You need to do some serious clean up on those connections.....there is a lot of corrosion going on there and it will plague you no end with electrical problems to leave things like that. I would not bother working further until this is cleaned up; pull each wire and clean the connections with fine emery cloth or sandpaper and then re-install with a contact protective compound like Dow4.
This starter relay is not likely your problem; reversing polarity to it would not cause any issues that would be obvious from understanding what the part does. Since you have cranking it is basically working A-OK .
First check your fusible link to see if it is blown open; it is there to help protect the car's wiring. The fusible link is the large red wire from the large terminal on the starter relay that is going to the firewall connector. This is easy to check: with the battery charged, do you headlights work? If so, then the fusible link is not blown.
After that I would suspect that your ignition module has been blown; it would likely be quite easily damaged with reversed polarity. Also, once the car is running see if the alternator is charging right; the solid state voltage regulator would also be a good candidate to be blown with reverse polarity.
Download your car's schmatic diagram from mymopar.com.