Comparing the part numbers of the two mice, this one – the cheaper one with part number 910-005672 – clearly is the refresh. Source: https://www.logitechg.com/de-ch...
Hello, no, I don't know the problem like that. Is it recognised after a restart? Otherwise, check the power options and leave USB on. Alternatively, uninstall g-hub and reinstall it.
The mouse is designed for Ambi-dexter, you can remove the G-keys and add two more on the other side. I can't say whether this works with the switching.