Sluta is intransitive, meaning it can't have an object, whereas the opposite applies to stoppa.
Furthermore, only sluta can mean "to end".
So I am a native swedish speaker, taking this test for fun... To me it is like this: Vi måste stoppa= We have to stop (We had to stop=Vi var tvugna att stoppa) :)
We have to stop is also an accepted answer. But måste is a strange word, it is used both for the present and the past tense. So in fact Vi måste … can mean both 'We have to …' and 'We had to …'. If you want to be clear you're talking about the past, many people do like you do and say *Vi var tvungna …' instead.
Same as in English. In reported speech at least, "must" is tenseless.
"She said that I must do it."
"One day you'll realise that you must grow up."
We often use other expressions such as "have to" or "be supposed to" for clarity.
To me, "She said I must" sounds ungrammatical (though not necessarily unnatural, as misuse of tense here is a common mistake). I would opt for "she said that I had to do it". Must is definitely exclusively present, at least in the English everyone I know speaks.
I think that their examples were grammatical, but I agree that must is present tense. "She said that you grow." In that sentence, grow is not past tense, as OP said must would be. Same deal, I think.