It means "then"

Maybe more of a "Hi later" or "see you later"

Does it have to make sense?

I thought the same thing

There isn't much of a difference it is still ater

Farväl is formal to the point where it would be very odd to translate 'bye' into that – if the English sentence had said Farewell it would have been OK.

Your friend is somewhat wrong. Språkrådet recommends writing it apart and says that although the form hejdå is common in practice, it's still only considered an informal version.
http://www.spraknamnden.se/fragor/arkiv_sprakrad_05.htm#hejda Both versions are accepted answers here though :)

It's correct, but it's only used when speaking is certain situuations.