TAKE (ME) DOWN= You make me feel small (you overwhelm me). The general sense could be that she has a big effect on him, making him feel very emotional and a bit disoriented. She is the one in control.

SPIN (ME) AROUND= To quickly turn your own or someone else's body to face the opposite direction. So he feels disoriented and out of control. = You make me crazy.

RUNNING ALL THE LIGHTS= Is like the idiomatic expression 'running red lights' which means to pass through an intersection while the traffic light is red without stopping. She got him speeding through red lights (traffic lights), setting the stage for their dangerous yet thrilling times.

LET ME INSIDE YOUR MIND= Let me know what you are thinking.

SUGAR= Sweetheart, honey, sweetie. Used to address someone you love /ʃʊgə*/.

I (JUST) GOT= (AmE) I (just) have. I JUST GOT THAT FEELING = I have an intuition.

THE SIRENS BURNING= Sirens burning evoke a sense of intensity, especially a sense of wrongdoing, however good the act of doing wrong may feel. It is the police car sirens, and if they are burning, they are working very fast and intensely, so the crime must be very important.  (see picture of sirens)

RED LIGHTS TURNING= If the lights turn red, that is usually a signal for danger, like alarms going off and turning red lights on. Also, it may refer to the siren lights turning around (they are red and blue, but the red colour is connected with danger)

TURN BACK= To reverse one's direction of motion.

HOLD ON TIGHT= If you hold on tight, you hold/grab someone or something to stop you from falling down. If you are driving a motorcycle or a car and tell your companion to hold on tight, that means that you are going to speed up so much that they will need to be careful not to fall down. So the police car is chasing us, but I'm not going to stop, so hold on tight because I'm going to speed up.

I DON'T KNOW WHERE THE LIGHTS ARE TAKING US= Here, the lights are signals guiding your way, like a plain landing, but he doesn't know if those lights are taking them to a good or a bad place, although he feels it is probably a bad, dangerous place because he then says "but something in the night is dangerous".

NOTHING IS HOLDING BACK THE TWO OF US= Nothing is restraining us or keeping us under control. If something holds you back, it stops you from moving or doing something.

DETAIN= Arrest. If the police detains a criminal, they arrest him and take him to prison (well, ok, to court). DETAIN may also mean simply to stop someone.

THE DANGEROUS= He is referring to the two of them, but this is bad grammar. "The + adjective" means "the group of people having that quality" (i.e. "the poor" = people who are poor), so "the dangerous" should mean "people who are dangerous", not just the two of them. Or maybe he means "the dangerous thing", but in that case it is bad grammar too because "dangerous" is always an adjective so it can't go alone, except in the aforesaid expression "the dangerous" referring to all those people. Unless he really is referring to dangerous people in general, in which case, it is good grammar.

I GOTTA= (coll. AmE) I have to, I must, I've got to.

BET= I bet = I am sure that...

TOES ON THE GLASS= This suggest somebody sitting in the car with their bare feet up on the dashboard, so their toes are touching the windscreen glass. It may feel super cool and relaxing but obviously it is a very dangerous position, especially in a car running so fast as this.

WHEEL= The steering wheel (the "ring" you use to drive a car)

WANNA= (coll) Want to.