Firstly I deleted TM and that didn' help. Than I uninstalled the driver, and started all over again, and to my rejoice everything was as it supposed to be. TM2 works without a hitch, without those weird (to me) messages. No trouble whole day, everything just works.

I must say, UCX II is a joy to work with, as is the TM2 software! And the ARC USB!

2. Deleting TM FX makes zero sense. Instead it should be cleared first what the current issue is.

3. For that we need proper descriptions of what's going on. Here the OP did not even tell which version of TM FX is currently in use (see 'About'), After installation of 2.03 old versions should be gone from the computer (especially the one in Windows\System32).

Anyway I'll try the first option, and if that fails, I'll try the second.
Thank you

So, what is the problem? You may delete TM by hand (first you have to fully close/terminate so that it is not running) and you also may uninstall the driver using Windows setup. And reinstall the driver again.

The action can't be completed because the file is open in TotalMix FX

(It is not opened, of course).

If TM runs it is considered open. And unless you exit TM using menu or taskbar, TM runs on background, so it is not possible to delete it.

And what TM have you installed? Which version?

So, to explain it again, more simply:
I installed the driver for UCX II, opened it to test is everything ok, and it was. Then I downloaded the new TM2 software, and then troubles started.

I just tried to do what Kubrak suggested, to just delete the file TotalMixFX_x64.exe, but message opened up:
The action can't be completed because the file is open in TotalMix FX

(It is not opened, of course).

And I wonder, how have you have achieved that two instances of TM run on your computer.

Having multiple RME  interfaces connect to the computer ? Does each device force Totalmix to open a instance (on Windows) ?

To me this is also unclear how many interfaces are there in the scenario.

Old UCX plus new UCX ll plus Babyface Pro FS ?

Recently I bought a new UCX II, installed its driver, and after that, the driver for TotalMix 2.

There is nothing like driver for TotalMix. You probably meant that you have also installed TotalMix. But TotalMix is installed together with driver for UCX II....

And I wonder, how have you have achieved that two instances of TM run on your computer.... TM in my experience checks at start if another instance of TM runs and terminates. So that, just one instance of TM should run, unless something goes really wrong.

RME driver for audio interface has uninstaller in Win (at least on my computer), TotalMix doed not have it. My guess is that it is uninstalled together with the driver. Otherwise one may delete TM by hand, just delete TotalMixFX_x64.exe file.

              Mismatch detected - mixer state of
     Fireface UCX II (1) and TotalMix FX are different.
 
  Click "TotalMix" to use the TotalMix settings (default) or
Click "Device" to convert the Device' mix into a TotalMix FX
                          mixer state or

Note: If unsure, click "Device" to check the unit's settings first,
      then hit Undo to restore the last TotalMix FX settings

                Device                            TotalMix

This was incomprehensible and very frustrating to me, and after a long hours of trying to make it work, it settled (as normal one TM), and I imported whole bunch of settings in it... But the next day, after turning up UCX & TotalMix, that "normal" version disappeared, and there was just one, "other one" which couldn't read almost any of my previous settings, and in the top left side it was text:
RME TotalMix FX: Fireface UCX II (1) - disconnected

To make things even worse, I cannot uninstall it! I thought I should try to re-install the driver, but there is no file to uninstall!!!

I'm using Windows 10 PC, which doesn't make any problems.
My previous device was Babyface Pro FS, and I uninstalled the driver before installing the new one, for UCX II.
Please help!