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Most of the questions on the main site are actual puzzles where the answers are guesses to those riddles, puzzles, rebus' etc.

I've become interested in certain puzzles, such as battleships, specifically in the uniqueness of solutions. From the linked site:

Each puzzle has exactly one solution, which can be found using logic alone and no guesses are ever required. If you think you've found another solution, then please double check the rules.

I would like to know if questions such as the below are on topic:

  • How do we know that the solution is unique?
  • Under what conditions are the solutions unique?
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    $\begingroup$ (There was a time where there weren't so many actual puzzles, and people answering them, on the main site; indeed, there was a brief period where those types of posts were actually not allowed! Relevant questions about puzzles, though, have always been on topic, even if these days they tend to be the significant minority. As long as they're not off-topic for other reasons, such questions should be fine here.) $\endgroup$ – Rubio May 8 '19 at 2:47
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Questions about puzzles are absolutely on topic here, even though as you say most questions are themselves puzzles.

I suspect that in many cases there isn't much to say other than "some puzzles have unique solutions, some don't, and when constructing one you need to verify that the solution is unique; the easiest way is by computer search", but there's certainly nothing off-topic about questions of the sort you describe.

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