Can this be rhetorical/figurative/romantic as well as literally refering to a future monarch?
Yes, it could be either.
The people who make these are so cute sometimes
How would you say "prince charming"? Like the one from a fairytale?
Swedish actually doesn't have a word for that. Even though it's a character based in fairy tales, and hence ultimately folklore, the English term is a much later concept and has never been given a consistent translation.
Personally I translate it as "drömprins" (literally: "dream prince" or, more liberally translated, "prince of dreams"), and Wiktionary agrees with me.
I agree - that's probably the best translation. Not quite a name, though.
Is the "s" in "prins"' supposed to be silent or am I just not hearing it?
Definitely not silent.