I have now used quickcure3, cured and original 172201000410.rgn - every time I get successful update (quickcure only takes a second or two while the others more like half a minute or so), every time the GPS restarts after the update and then shuts down, never visible to the PC except for if I turn it on in pre-boot mode then I can hear the "ding-dong" as when you plug in every other USB device.
Whether you use QuickCure or Cure3 to enable Mass Storage Mode, you MUST either remove the wrong file loaded by GarminExpress OR re-format with RMPrepUSB as I said earlier. Then you load original firmware to enable the device to boot. It will never boot fully with a cure firmware loaded, that's it's whole purpose to stop the boot process without loading corrupt or wrong files so that they can be removed or the file system re-formatted. Once that's done, then original firmware MUST be loaded so that the device can operate normally and be updated.
Only things I'm not sure about, even though I have read a lot on this forum, is the use of quickcure3, what I did was to rename it to 172201000410.rgn and loaded it to updater.exe - thought that was the only way. Also, after this, it should be enough to just turn on the GPS to have access the file system??
Yes, the usage is simply re-name QuickCure3.rgn appropriately as you said and flash as detailed in the cure thread. It doesn't use the actual device's firmware at all. It relies on finding a copy of bootloader in the device memory, if that's not possible then it doesn't work and you must use cured firmware to enable MSM to access the file system. Both QuickCure3 and Cure3 when loaded result in the boot stalled on the logo screen and the device will stay like that until original firmware is loaded.

I don't think WebUpdater plays nicely with Asian devices the same as you've found with GarminExpress. It also seems that you've got the two devices confused going by the different UIDs shown in G7ToWin and WebUpdater. You should remove those UIDs from the pics by the way, as it'd be easy for someone to use either or both UIDs to 'clone' a device. As evidence of that, see images below.

Try to update it using the Asian-specific tool Garmin Updater (which is not WebUpdater). Garmin Updater was initially downloaded and invoked by starting Laucher.exe. If you've already got Garmin Updater you'll find the EXE to start it in C:\Program Files(x86)\Garmin\Garmin Updater. Look for "Garmin Updater.exe" and double-click it to run it. If you have a 32-bit OS then it'll be 'Program Files' without the 'x86'.

Using Updater

Don't worry, I cancelled the update and deleted everything. I simply wanted to show you and other users how potentially dangerous it is to leave UIDs in the public view. Anyway, that will give you an insight into how to use the Asian Updater, step-by-step. After the updates have downloaded, you'll get another screen asking you to remove some files from the device (as you clearly have Mass Storage Mode now accessible you can do that) and then proceed. The files that were loaded to the PC will then be transferred in proper form to the device.