When should I use 'av' instead of 'om'? I can never get my head around the versatility of the word 'om' in Swedish.
I understand that like this: av means "is part of" whereas of means "out of". In German you can help with av=von and om=um
Does this sentence imply that something is west of the capital, as in not on the western side within the borders, but outside of the western boundaries?
Yes, it's definitely outside the capital. If it's in the capital, it's i västra delen av huvudstaden or something like that.
is huvud in swedish like the german Haupt? huvudstaden - Die Hauptstadt?
Huvud exactly means the important part specially when it is laying on top section
"Väster om huvudstaden ligger en stor sjö"
"West of the capital, there is a large lake"
(or similar constructs like "There's a large lake to the west of the capital")