Learn Swedish: När flyttade ni in? - When did you plural move in?

This is because of the V2 (verb-second) rule. Since the sentence starts with the question word när, the verb must take the second position, pushing the subject ni to the third spot.

Is ni used for one person or multiple people here?

In modern Swedish, ni is the plural you. If you were asking just one person, you would use du instead, making the sentence När flyttade du in?.

Why is in placed at the very end of the sentence?

The words flytta in form a particle verb, meaning they work together to create the specific meaning of moving into a home. In sentences like this, the particle (in) is separated from the verb and goes after the subject.

Where should I put the stress when saying flyttade in?

In Swedish particle verbs, the stress always falls heavily on the short particle word. When speaking, you should put the emphasis on in rather than on the main verb flyttade.