I still don't see any clear sense in all of that. Некоторые - just "some", несколько - just "several" without any existential metaphysics.

All I can is to provide my own comments about the stuff.

"Ни-" pronouns provide negation:
1) Negative when used as separate sentences.
2) Otherwise do not contain negation by themselves but used only with negations.

"Не-" pronouns provide uncertainty of all kings. (Usually stronger, more emphasized uncertainty than "-то", "-либо", "-нибудь" pronouns.) Некоторые - "some of them but we don't know (or don't want to mention specifically) which exactly" etc.