You need a 125R resistor between the pin 5 and the gate of the FET.
You need a reverse bias diode across the relay.
You need to connect the -ve of the battery to the arduino ground.
1) How did you calculate the size of the resistor and why is it needed exactly.
2) Do I need a reverse bias diode because of how the transistor is wired to the relay?
3) I did the sketch pretty fast, I will ground the Arduino to the battery and make a 5v regulator for the (+)
I'm just starting to get into this stuff so go slow

Thanks so much,
Andrew
what are you trying to do?
Use an RFID reader to act as my ignition switch (or kill switch), since I have no key.
I guess I could use a smaller Relay, I just have this one laying around.