No, it is not an F. It's a sj-sound. If phonology isn't your thing and the sound example in the link doesn't do it for you, think of it as something like the German and Scottish ch-sound (in "ach" and "loch"), but lighter.
Exactly, sin always refers back to a subject in the same sentence. So pojken sjunger för sin katt means that 'the boy sings to his cat'. But if she sings to his cat, we'd say hon sjunger för hans katt.