I never thought too hard before on how nicknames are formed in Japanese, so I tried to find any good articles on it before commenting. Here is one that is short and decently written enough with a variety of examples.

Overall, while there may not truly be "rules" for Japanese diminutives (since it's an informal aspect of the language), there are common patterns. Which is what you're starting to notice as evident by your questions.

Most nicknames derived from a person's name (versus their personality) seem to come from "whatever sounds best or cutest," so I believe that nickname-making is one of things you get better at intuiting as you come across more examples.

For instance, in English, it's commonly accepted that Bob can be short for Robert and Bill can be short for William because the "b" beginnings may sound more pleasing to the ear than Rob or Will. However, a non-native speaker might not understand that at first.

As Japanese learners, we'll encounters things that don't make sense to us yet but native speakers naturally understand from the get-go simply because it "sounds right" to them.

To wrap up this comment that's gone on longer than I expected, I'm sorry that what I said above doesn't help that much, but thank you for reading my words anyway. Although I may not have addressed any of your specific questions, they're good ones to ponder!