Can högskola mean highschool, e.g. age 11-18, or is it reserved for tertiary education?
No, högskola teaches the same level as university. Only institutions of education with a sufficient degree of own research may however be styled universities. I'm not sure as to what tertiary education means, but after brushing through its wikipedia article, I'd say maybe. Högskola/universitet refers to tertiary or higher education.
Swedish school is divided into grundskola years 1-9, gymnasium years 10-12 and then högskola/universitet from then on.
Is "gymnasium" more of an elective school that students attend to prepare for/test into college (ie, students that opt out of attending it would go instead to a technical or vocational school)?
No, all schools year 10-12 are called gymnasium. They may have different orientations though, such as techical school, natural sciences, media, agriculture etc. The number of people who don't go to gymnasiet (definite form) are negligibly low.
Does the högskola typically offer a degree? Is is completely different from folkhögskola?
They are completely different because högskolor/universitet give academic education. Folkhögskola (folk high school) offer many types of shorter or longer courses for your personal development in different fields, eg. theoretical, vocational, arts studies.
So is folkhögskola like a community college? (In case you don't know what that is, it's basically a college were you go to only earn a 2 year degree. They funded by the state so their normally cheaper but they don't usually offer as comprehensive a degree program as a college/university)
it's like the difference in a college vs. university in the US. you can get a degree from there, and they have many of the same programs as universities
College and university are near synonymous in the US. The biggest difference between the two is that universities tend to have more graduate programs than colleges, but both teach to undergraduate students.
Yep, it's a false friend in that respect. But it's important to get to know the false friends! :)
Because university and college are two different things, I think. Or at least they are in England, I don't know about Sweden.
Former exchange student here, there seems to be a bit of confusion here, but a högskola is similar to a community college or vocational school, and a folkhögskola is for vocation, arts, etc. And these days also offer alot of courses and programs for swedish culture and language for immigrants and new residents. For example, I went to a wonderful language camp at a place called Ädelförs Folkshögskola which also seemed to offer things like elder care. So its almost like a combination college and community center, at least in this instance.