I read in the manual, that u should charge it with 5V and 2.5 amp, but im not sure. I already read, that a undervoltage can damage the pi and that USB 3.x would be enough, but I still dont know how that is with a USB charger that is connected to a wall socket and not with a USB port of a PC.
As mentioned in the comments, your choice of words suggests that a clarification is needed:
Batteries are charged - a RPi is powered
A USB power supply that plugs into a wall outlet will work fine if it can source 2.5 Amps. The power supply should have this specification printed on the housing, or embossed in the plastic body. You don't necessarily need a USB-3.X supply - just make sure the supply is capable fo supplying 2.5 Amps. You may even be able to get by with a bit less than 2.5 Amps if you don't use peripherals that draw power; e.g. disk drives.