the generator and the surroundings get really hot, so hot I cant touch it longer than 1 second.

the generator gives the right amount of voltage and the battery is in good condition.

so, what can make the generator, airpump so hot? or maybe it should be that way?

 

If by generator you mean alternator and your car is near stock, its not surprising it gets to hot to touch after driving the car. Hey man that 13B is just cranking out the heat.