Wiktionary says that "kräva" translates as "to demand, to forcefully request".
The Swedish Wiktionary is probably more accurate, but my Swedish isn't good enough to work through it (I tried and ended up with 10 tabs open explaining new words in words I still don't know).
Folkets Lexikon suggests "åtrå" or "längta efter" ("long for", maybe?) as translations. There's no entry on the English Wiktionary for "åtrå", but there is on the Swedish Wiktionary. I had the same problem as above for the Swedish, although åtrå does seem to be permissible in a sexual context? Can't tell, sorry.
You're right, längta efter or maybe sukta efter are better translations of crave, 'kräver' is a false friend. And åtrå is most often used about sexual desire.
Why is it tied to "frihet"? I was under the impression that "sin/sitt" always referred back to the subject of the sentence.
Correct, but those are two different processes. You use sin/sitt to show that it's their own, but it still needs to agree with what it describes.
Put another way, if you have the sentence "The king wants a table", you would translate that as Kungen vill ha ett bord even though kung is an en-word.
if "kräver" means demand then how would you say this: "the people require their freedom"