What pages on your site need to have OpenGraph & Twitter Card images / meta tags?
All of them? Just the main ones?
Even the pages behind logins, pages that require payment to view, HTTP error pages, login, logout, change password, etc. ?
OpenGraph/Twitter meta tags should be used on any page that anybody is likely to send to someone else on social media or in chat apps. This is the tags' purpose - they make the link appear nicer on social media sites and chat apps.
In practice, this means that all your public-facing pages should have these tags if possible.
Pages behind logins
No, if they aren't for the public to view.
Pages that require payment to view
Yes if possible, as people may still share these links on social media. Though if you do this, make sure the tags themselves show up without needing to log in, because crawlers will not log in when scanning for tags.
HTTP error pages
Not required. People don't share these on social media.
I would say yes, since someone might share a login page on social media.
No, since there's no reason to share it on social media.
Yes, someone might share that link.