STM32 USB device - device descriptor request failed
I've solved the issue. I don't know what the problem was, but I did another project and now everything is working perfectly.

To make this post a bit more valuable to others that may find it: At beginning I used a program generated via STM32CubeMx - and it has the problems described here. I was suggested to download STM32F7Cube (Cube not CubeMX) and use the examples from there. I did that and everything is working.