not really. for example "Moc" is also "Force" in Star Wars. Force normally is "siła" also superheroes "powers" are "moce".
"Mam tę moc" fits with rythm of "Let it go", also superheroes "powers" are "moce".
What "moc" is not - is not ability to rule someone else- that is "władza".
So "Mam tę moc" is not about Elsa's power as a queen, but about her ability to freeze the world.
I've never watched the movie, but I did listen to the song many times. I believe it's the strength of her spirit, freedom to do what she wants. Or you might treat it blunt more liberal and consider it a power over ice (though the other interpretations are more fitting in my opinion).
Well… While there's no difference in meaning of adjectives "sławny" and "słynny"(in dictionary entries), the verbs "sławić" and "słynąć" do have different meaning and in common use(at least my use, that is ;-) ) meaning of those verbs somehow "creeps" into the adjectives, so I would agree that "sławny" is generally positive while "słynny" not necessarily so much.
Also, "słynny" in my opinion can be used for people(and things) that are known for just one thing and not necessarily generally famous, like for example former MP Kracik, who is totally gone from general public space(unlike a few other former MPs like Rokita or Kalisz) so I would never call him "sławny" but nevertheless he is "słynny" from "Kracikowanie prawa"(making law in a "Kracik manner" or Law à la Kracik), that is using the letter of the law without paying attention to logic(in this particular example, it was passing the government budget as minority motion in Sejm, iirc).
Anyway, that's just my opinion and description of how I actually use those words - dictionaries do not agree, as immery already pointed.