How fast can printer head move without damaging steppers? Is there any risk of damaging stepper motors if I set too big travel speed?
What is maximum safe travel speed?

My printer is a German RepRap Neo.

I currently use 120&nbsp;mm/s. Is it safe to increase this value to 200&nbsp;mm/s?
What would my printer do if I set very big travel speed?
Short answer no

We use stepper drivers to limit the current, the travel speed is at capped by the amount of current supplied by the stepper drivers. This prevents the stepper motors from damaging themselves. You can set 200mm/s in the slicer, but you have no guarantee that that will be reached in real life.

One thing to keep in mind though is that setting your travel speed too high can induce artifacts such: shifted layers, ghosting, uneven extrusion, etc. So the best thing is to keep the speeds within the specified limits.