Pass is masculine (der Pass) but Visum is neuter (das Visum).
The two things you need are the objects of brauchen, so you need accusative case.
The masculine accusative form of ein is einen (with -en like den), but the neuter accusative form is ein (accusative is always the same as nominative for neuter things).
So, nothing to do with und. It would be the same in Ich brauche einen Pass or Ich brauche ein Visum or even Ich brauche ein Visum und einen Pass.
If "Sie" is formal "you", then should it be "brauchen"?
Yes. The formal Sie acts grammatically in all respects like the pronoun sie which means "they", except that Sie "you" is capitalised.
Thus you need a third-person plural verb form with Sie -- even if you are just speaking to one person.
Since sie can be either you or they how do i know which one to use?
Lower-case sie can never be "you".
But at the beginning of a sentence, you can't tell the difference between sie brauchen "they need" and Sie brauchen "you need".
And so both translations will be accepted. You can choose either one.
You don't have to read Duo's mind to "know which one to use", since either will work.
It certainly uses the same verb forms and pronouns as "they", yes. (Except that pronouns and forms thereof are always capitalised for the polite "you".)
English sort of did this as well -- "you" used to be plural only, then used for polite singular as well, now it's used for everyone and "thou" has pretty much died for most speakers.
When sie is used to mean "you", it's capitalised for politeness: Sie.
It's more polite because it's less direct.
Consider Italian, which uses "she" as the polite pronoun, presumably from a feminine noun such as "your grace" used as a polite version of "you"; and Spanish Usted is from "your mercy" (vuestra merced).