Yes but if the header is present you already know the user will not consent so there is no need to even ask.
Exactly. So if the header is present, don't ask because it's a no. If the header is not present then ask the users consent. Easy as pie
Yes, it would need to be a header saying "I authorise".
A technicality on linguistics in this case as a header would still satisfy the requirement.
EU should've mandate that providing the header is enough. And no window should be shown in this case (you can still ask to allow on top of a page, but it should not be overlay). And yea, it should _never_ be an overlay, because overlays is a predatory design practice (EU, please, could you be useful one more time?). Except after GDPR web designers gone mad and we have modal overlay windows for cookies, for newsletter, for ads (always had these), for paid subscription, for go follow us on Twitter.
But you can ask a user at browser install, if they want to be trackd or not, so it's one opt-in/opt-out for all pages.