Does this sentence really means both "She does not eat meat" and "She is not eating meat"? It is quite ambiguous as she might be vegetarian (never eats meat) or just that she is not eating meat right now...
It means both; Swedish does not distinguish between simple present and continuous. If it's necessary, we can always clarify by saying Hon äter inte kött just nu ('She's not eating meat right now') or Hon är vegetarian ('She's a vegetarian').
In slavic languages continuous and simple tense is not distingiushed as well, so it's pretty normal ☺
Of the ones I've poked at, Turkish, Japanese, and Hindi do, and Chinese can mark an action in progress with 在.
Does initial /k/ always sound like an English sh? It seems very odd to me...I keep want to associate it with 'a cut of meat and give it a /k/ sound here...
Generally, k is pronounced /ɕ/ before i, e, ö, ä and y. However, we have a lot of loanwords that makes it a bit harder. For example, "att köra" (to drive) is pronounced with /ɕ/ while "en kör" (a choir) is not. Other examples of this are "keps" (cap) and "kö" (queue/line).
I don't doubt that, we've had lots of comments like that recently. If it happens again, I would appreciate it if you could leave an error report or a screenshot so I have something to share with the developers.