Not quite. She may have several ex-husbands, but only the last one of them is her previous husband. ex-husband in Swedish is exmake, exman or före detta man.
Is "man" being used like when woman in America say "my man" or is this "man" in Swedish a literal translation.
Not really, there are other words for that. min man in Swedish means that you're married to him.
That's odd, it's definitely accepted. Was it a "type what you hear" exercise? Those can only accept one solution for technical reasons.
Reading the rest of these comments, I wonder if her last husband might not be the best (of many) translations. That definitely would refer to just the most recent ex.
It could also mean her last ever husband, which would be Hennes sista man in Swedish.
Why in one of the previous expercises we used 'förra veckan' (definitive form), but here it is just 'man'?
When something is 'owned' by something or someone in the genitive case like here, hennes, we can't have a definite form after that. It's the same in English actually, you can't say her the previous husband.
I think "former" here is going to have the same problem as the one Arnauti points out with 'ex' - a former husband could be any of the ex husbands, whereas "förra" is supposed to refer to the most recent ex, as it were. (I'm actually not so sure that 'previous' doesn't have the same problem as 'former' or 'ex' here, but that's a worry about English, not Swedish.)
I can't really think of a difference, but it's usually more idiomatic to use förra.