Make sure the new battery is working correctly. It should measure about 12.6 volts in the morning after the car has been sitting overnight, and immediately after starting the engine in the morning, 13.5 - 15.5 volts. With these symptoms, for the latter test, it is a good idea to probe at both the battery posts and the battery connectors. There shouldn’t be much difference. What do you measure?
UPDATE - Went out and bought a OBD2 Scan Automotive Diagnostic Tool Code Reader. Can’t tell you what the codes said, it gave an option to erase all codes so we thought sure why not. All lights off and the car is driving normal as far as the RPMs. I know this doesn’t solve how screwed up the car is and the problems are still there, but it makes it drivable for now and we can now work in the issues one by one and still be able to get to work.
Thank you to everyone for your help!