A:Answer No, I don't think so.
I just checked in the Google Home app and it seems that routines can only be triggered in 3 ways:
1. Voice command,
2. Time, or
3. Sunrise / sunset.
So pushing this switch cannot be used as a trigger for a routine, as far as I can tell.
This is one of the reasons why I installed Home Assistant recently on an old laptop so that I can create all types of fancy automations in my house, including using this switch and other smart devices made by TP-Link or other companies.