-What are they supposed to validate?
-If they are not working or outdated, why are they there?
They validate the HTML markup & CSS against the various standards set by W3C (depending on the version). Errors/warnings are somewhat common for most websites though. I'm guessing the links/icons are there because they are part of the footer SMF uses (forum software), unless theymos added them at some point.
They don't work because browsers don't automatically send the referrer when coming from https to http, so the URL would have to be included in the link:
(edit:.. or maybe https could just be added into the existing link)
https://validator.w3.org/check?uri=bitcointalk.org
https://jigsaw.w3.org/css-validator/validator?uri=bitcointalk.org
As for your last question... I doubt anyone really cares about these links.