Everything works fine but when I speed up cycle things get messy (I need speed about 30 Hz). Solenoid coil can't discharge properly that quickly (it has delay).
It's usually the physical inertia that limits the speed of a solenoid. In theory the inductance could be a factor too, but I'm pretty sure the big issue is the mass. 30Hz is slow for electronics but fast for a solenoid or relay.
I am also afraid of over-heating due to quite high current
Overheating of what?