OK guys, thanks for your suggestions. Finally I got Ubuntu Touch installed!
Unfortunately I'm not able to say what especially was the case.
What I did:
On my Linux Mint computer I removed everything regarding UBPorts installer.
On the deice I've additionally removed developper option "check for apps installed via USB for harming behave".
Then I installed UBPorts installer again (0.8.8) and started flashing again. After flashing I've had the same effect "Searching for device", but I saw for a short moment "Ubuntu" on the device screen....
So I unplugged the device abut it stuck on the screen "Redmi by Xiaomi unlocked" - so far the same as before.
Now I've made a manual reboot on the Redmi, and surprise, after the screen above, "Ubuntu" appeared and started.....
What's not nice:
The device starts now with "Redmi by Xiaomi unlocked" (ca 5 sec.) before ubuntu system starts.
Seems to me, that UBPorts installer just was not able to send reboot command to the device.
After two days with Ubuntu Touch, I'm very satisfied. Got all what I've expected.
UBUNTU TOUCH ROCKS!