In general, site features are acceptable for use in, and/or as the subject of, puzzles. We've had many puzzles where clues are hidden in edit histories, as well as puzzles about up/down votes and reputation, fake-duplicate and fake-deleted posts, loads of puzzles where PSE users are involved¹, and even various historical versions of the Stack Overflow 404 page. Feel free to be creative in incorporating aspects of the site into your own puzzles.
Do be cautious about referencing things that are likely to change. In an earlier site meta post, Is it OK to use specific users as part of a puzzle mechanism?, we point out that users can always change their names, avatars, and "About" information, or even delete their accounts entirely.¹ Referencing anything in your puzzle that may change over time could render the puzzle unsolvable in the future; the more likely something is to change, the more important it is that if your puzzle relies on it, that you include it in your puzzle rather than just referencing it. This is a big part of the reason why we want puzzles and their component parts to be self-contained—to prevent external references from going stale and rendering the puzzle incomplete. References to site features should be treated with similar care.
The "Hot Network Questions" list, for example, can change with every page load, so if your puzzle is based on its contents, screenshot it and include that in your puzzle somehow. The name of the site, on the other hand, is particularly unlikely to change, so relying on that is pretty safe. Other things fall somewhere along the spectrum. Do your best to future-proof your puzzle against things external to your puzzle post changing or disappearing entirely.
Having said all that, things posted to the site need to be per se acceptable on the site. Creating a new tag to be part of a puzzle, which doesn't otherwise stand on its own as a suitable tag, would not be okay—and the likely result of doing so would be the tag being deleted as unnecessary, and the consequent breakage of the puzzle which the tag was created to support. A post that appears to not meet site guidelines would run a very real risk of being closed, so approach such ideas cautiously; you want to make sure people won't be so fooled by the surface your puzzle is hiding in that they never reach the puzzle itself.
¹ It's unwise to put another user into your puzzle in a way they might object to, so it's always safest to ask them first. And be careful that your puzzle does not rely on the assumption that the user you're referencing is well known; keep in mind that not everyone who encounters your puzzle, now or in the future, will even recognize the reference as a Puzzling user unless you've sign-posted that well, and a user who is well-known today may not still be well-known, or indeed even still an existing user, five years from now!