I think not. shall is accepted because it's ambiguous: it could mean will. But should has a modal meaning that would be borde in Swedish.
What if i want to ask if I pass (as someone)? Would that be 'ser jag lik ... ut?'
Passing in the trans sense of the word is passera in Swedish, I'm not sure about passing as a specific person. If you speak about getting into events with age limits of different kinds, people would usually just speak about komma in instead (like, when they let you in to see a movie where the age limit is 15 but you're only 13).
(super late answer) None, both are said as dom by the overwhelming majority of speakers.
Shouldn't it be, "Passerar vi genom dem? " for "Are we passing by them?" and "Passerar vi dem? " for "Are we passing them?".
genom only means 'through' as you could pass through a city or doorway. It's possible to add förbi in Swedish here but we're more likely to say just passerar vi (even in many cases where you'd want 'by' in English). On the other hand with verbs like går förbi or åker förbi (like, 'walk by' or 'drive by'), of course förbi is absolutely necessary to get this meaning.
In English, "We are passing them?" is an acceptable casual question, but a better translation from this Swedish would be "Are we passing by them?" or "Do we pass by them?"
Is that really a question? Sounds more like a statement: "Vi passerar dem."
No. By putting passerar before Vi, the sentence is turned into a question. Like the difference between Vous avez and Avez vous in French.
I read that we are passing the others, in Swedish. But in the English translation I read that the others are passing us? So in Swedish we walk and the others could standing still, and in English we could standing still and the others are walking. So in my opinion the English sentence would be:"Are we passing them?" without the word: "by"