Hey, I'm doing maths tutoring in person as well as online. In person I write or draw on a piece of paper (yes, totally without electronic parts), online I use an old Wacom tablet and some online whiteboard.
Would it be possible to use a remarkable for both purposes? Writing on it with the pupil next to me and sharing the content afterwards on social media or anywhere in the cloud as well as writing on it while in an online session (like Teams or Skype ...) and sharing the content live (is there any PC or laptop connection possible and use screen sharing in Teams or Skype?) and saving it to also share it afterwards...
And does it offer any maths templates like coordinate systems or the like. Or is it possible to create templates on one's own?
As long as a PDF is okay for "sharing afterwards", yes.
As for "sharing live" ... I use goMarkableStream for this. You view the tablet in a browser window, and you share the browser window using whatever video sharing software you're already using for the meeting. It works by talking directly to the tablet and does not require a reMarkable Connect subscription or an internet connection (i.e. it can work over a USB cable).
Just be sure to install the correct version of goMarkableStream, depending on the firmware version in your tablet. There are now three different ways for software to access the screen's contents, and each version of goMarkableStream implements only one of them. This is explained on the Github page where you can clone the repo and/or download an executable.