No, not really. When speaking like that in Swedish, you mean your husband.
I think so since, at least to me, it would imply that he is coming back to Sweden from a trip to Finland. But I guess it's a bit situational.
We've discussed it internally, and it's not a clear-cut case, but we've ultimately decided not to accept it. It only really works idiomatically if you add something more to the phrase, such as "... next month".
The comes from either means is from there originally or (less likely) is a likely completed action travelling from there (without further context). Is coming implies future or in process of coming, and never means hails from.
It would be more appropriate to say "Min make" instead of "Min man" if you mean they're married. The latter choice would also translate to "My man", even if it's more of a general way to describe your partner.
I don't think so, man would be my first choice for husband and I don't think I ever use make in speech. I could imagine that make would be preferred in Finland, but other than that I don't know.
I wrote "My husband hails from Finland" and was marked wrong. However, I disagree. I think "hails from" is a quite commonly used term in English.