A user of my site(JavaScript) often needs to create an event on his profile calendar (on my website) and send it also to his Google calendar, he does not log in with Google Accounts but he can give me authorization to get access to his calendar data to insert, remove, list and update events; so I can store an refresh token for when I need to access data (private, public).
Google documentation lets us create event as on this Link; for calendarId, it suggest to use the "primary" keyword for the currently logged in user; also I can use the calendarList.list method to get an email of the user's calendar.
But even with this method. I don't find a way on how to use a user's refresh token to retrieve calendarId and insert his event on his calendar for the logged in user without Google Account.
Is it possible, using Google API, refresh token and access token to retrieve calendarId and insert an event?
If the user is using his Google Calendar to insert events, then it will sync to his account wherever he opens it. I suggest that you stick with using Gmail address tho to avoid these kind of hurdles.
Check the Javascript Quickstart for the supported way of using Google calendar API. If it's not stated, it might not be supported.