I remember än meaning "yet." But I don't think I have seen ännu yet. When should we use ännu?
Is that only in the case of 'yet', or could you say 'än bättre' instead of 'ännu bättre' too?
I've seen in some places (like Wiktionary) that "än" is generally used for positive statements and "ännu" for negative ones to mean "yet". Is this not the case?
I think they're pretty much interchangeable, it's more that there could be some personal or regional preferences. I'd prefer än in all time senses, but for the comparative, I'd say ännu bättre and not än bättre, although both are acceptable.
"the invites" is used in speech more often than "the invitations" where i come from in NE England, but this was marked wrong :(
inbjudning is out of fashion except very colloquially, it's mostly used in compound words such as inbjudningskort ("invitation letter"). But there are still people who do use it, so it's certainly not wrong.
"already" means something occurred sooner than you had expected it to.
"yet" means "until now", normally with an expectation that something will happen.
So you can say "She already ate the candy", but not "She yet ate the candy."
And you can say "Has she eaten the candy yet?" and it will mean you're simply asking if it has happened - but you can also say "Has she eaten the candy already?" and it will mean you're expressing surprise that she ate the candy sooner than expected.
Swedish redan works like "already", and än like "yet". They don't correspond 100% perfectly, but they generally work the same way.