Whats the difference between stannat and slutat?
Generally speaking, stanna is for bringing a movement to a halt, while sluta is for ceasing to do something.
Though it sounds weird without a context, is "We have stayed." a possible translation?
Yup. Like you say, idiomatics aside it works well. The third accepted option is "remained".
Stay/Stop. In English we stay an execution (which means it won't happen).
And court cases can be 'stayed' in English too, meaning they remain unresolved and temporarily stopped.
can we use this one for like stopping some habit you had before like I have stopped smoking the cigarette Jag har stannat röka cigarett or you have to use sluta Jag har slutat röka cigarett which sentence is correct?
No, you can't use stanna for that sense at all.
So, is stanna intransitive and sluta transitive?
sluta is intransitive and stanna can be either. There's also stoppa which is transitive.