That's what I thought about 1 and 3
(When I meant being able to see the list of badges for non-admins, I meant that admins could take a look at the list of all achievements in badge customization, but others can't, so if there was a special page that listed all badges that could be earned for them to see.) Thanks for the link to Badges Wiki. I didn't know about it.
About 2.
I don't necessarily mean a custom track.
However, this one definitely seems to be a custom track as I don't see it mentioned in the Badges Wiki.
Templates Edit track can be enabled or disabled with a checkbox. (Although it can be customized with different names and images like the rest of the badge tracks).
I know it is active because it had been enabled when the achievements were enabled. I can see it being enabled (I'm an admin in the wiki). It was also gotten by one person quite a while ago.
But since then, it seems bugged, judging from what you say. This is because no kind of edits to Templates or template documentation in said category, neither new edits to pages in the Templates namespace, are triggering the achievement.
I'll try asking Fandom about this, as this likely affects custom badges only. I appreciate your help!