So there’s two sets of white red and black wires, one set from the steering servo and one set from the esc. The ones from the esc are the ones that look fried, the black one in particular. Will this mean the esc is also dead?
If I had to take an educated guess Id say your ESC is fried. More than likely its what took out the receiver in the first place. You can try and replace the connector and see if it still works but you might lose another receiver doing that. Your call. If you choose to replace the ESC you can get a
Hobbywing ESC which is a decent budget brand. You can get the
10BL60 SD which is just adequate for that kit on 2S LiPo (which is what it comes with) but personally for like $8USD more you can get the
10BL120 SD which can handle twice as much current. Who knows, one day if you ever wanted to give the Bugsta a kick in the rear, you could put a higher KV (faster) motor in it and that ESC would be able to handle it. The 10BL60 can't handle much more than the 2950kv motor thats in it already.
Have to add on the plug for the three smaller gauge wires that go to the battery (not the fat bigger gauge ones) there is one that is brown at the pin (the red wire)
The plug you are referring to here is called the balance plug. This plug is plugged in to the lipo charger so that the charger can make sure the 2 cells inside the battery are charged evenly so one doesn't get over charged/over discharged. That and checking cell voltages are the only things this plug is used for. Take your volt meter and take a DC voltage reading of the red wire and the wire in the middle which appears to be the black wire. Then measure the voltage from the middle (black) wire and the last (blue) wire and let us know what the readings are. This will give us a rough idea if the battery is any good or not. Also make sure the lipo feels solid and flat. If its squishy or puffy then its no good.
You will need a lipo charger to charge that battery. I'm assuming you dont have one yet. Personally I recommend the
Hitec X2 AC Plus. Its not the cheapest charger around but its extremely capable for the money. Other people will offer other recommendations but we can discuss that later when your ready to buy one.
Just FYI, You can buy extensions for the balance plugs to make it easier to plug into the charger cuz the lead on the battery is quite short.
If you're saying that you need to replace the plug on the battery because of the scorch mark, you can do that. The connector is called a JST-XH connector. You may not need to though. It looks like the plug is still probably functional, assuming that the wires and the plug inside are still intact. Something shorted that out though at one point which makes me question the batteries integrity but lets see what the volt meter reads on each of the cells and go from there.
Can’t I get a receiver that will work with the controller it came with? I believe it’s 2.4 ghz already, that’s pretty much where my knowledge ends so far bud haha
The manufacturers website has a few replacement parts for that car but a receiver isnt one of them unfortunately. This is often the case with cheap Chinesium RCs. What parts are available can be found
HERE.
I believe you can buy the receiver from the manufacturer of the radio though. Check and see if
THIS is your radio. If it is then the receiver is also on that page below it.
I second the vote for a Flysky GT3b as a good budget radio option. Receivers for it are cheap ($10 USD) and you can use the same radio on as many as 10 different RCs provided you have a Flysky receiver for each car you want to control.
especially when I’m trying to sort the two nitro cars I have already haha 
