It might be a coolant leak in the heater hoses or possibly the heater core. Most vehicles have a shut off valve in the the heater lines so when you aren't using the heater coolant is not going through lines enough for you to smell it. I would look for a leak and definitely look at the valve in the heater hose, those tend to leak. Good luck
I would replace the oil pressure sensor. If it fails the fuel pump will turn off. The oil pressure sensor is hooked up to the fuel pressure relay and if you don't have oil pressure it will kill the fuel pump relay which will turn off the fuel pump. This is to stop the engine from damage if you lose oil pressure. The way it's been acting it sounds like the sensor. That's where I would start, I would get a fuel gauge and check the fuel pressure. I would also get a scanner and check for computer codes. I'm don't know what mechanical skills you have but GM vehicles have a test port in the fuel line on the engine. Autozone might be able to lend out the fuel pressure gauge. When you turn the key on to the rin position (not start) it will give the fuel pump a 2 second power signal to prime the fuel line. After that you will have to crank the engine to get fuel pressure to come up. You will have to look up the fuel pressure for your vehicle. If the fuel pressure doesn't come up it's most likely the oil pressure...
Could be the charging port or possibly the tristar chip might be bad. You need to try and charge it, it might not be making a connection to the charging cable. If it's been opened the charging port might be unplugged. It's hard to say unless you open it up to make sure everything is connected inside.
It could be multiple issues. Check the charging port for debris like Lint. It could be the charging port. It could also be the tristar chip. I would also try a different charger. I would recommend taking it to a repair shop and have them check the tristar chip, it's simple test .