Jag har längtat efter dig. Varför inte?
That'd be "I have been longing for you".
So here we mean we were missing you as in the police and the neighbours are involved
No, what's meant is that the person speaking missed the person spoken to, as in longing for a friend who's been away for some time.
Correct me if i'm wrong, but in jordskott, when they were looking for the kids the sign said "Saknad", which would come from this word. So it works like the english word missing, i guess(could mean either )
Ah, yes. The past participle means missing as in your first example.