> If I want a cookie to be only sent in requests from a page on
https://mywebsite.com to
https://mywebsite.com/internal/..., but not from any other origins, should I use Lax or Strict?
Strict. If you use lax the cookies would be sent when clicking on a link cross origin.
Most people however do want cookies to be sent on cross origin link navigation.
[Edit: someone else pointed out that you would still get cookies from requests sent from subdomains, and indeed that is what the article is about. For lots of people that is probably not a big deal]
> If I use HttpOnly cookies and Access-Control-Allow-Credentials=false on https://mywebsite.com/internal/..., does that make SameSite irrelevant? Would there be a security risk even if SameSite=None? Is the only security risk related to <img>?
If samesite=none, (and you didnt implement csrf tokens) you could still send cookies from other sites via forms. So you can pull off old style csrf (like how you would exploit a csrf in the 90s before ajax was even a thing).
Also i think (but not 100% sure) that cookies would still be sent for ajax requests not requiring a preflight or for script inclusions.