Novi stanar se uselio sa porodicom.

Because novi stanar is the subject of the sentence, so it is in the nominative singular. The adjective novi must agree with the noun stanar in gender, number, and case. Since stanar is masculine singular nominative, the adjective is also masculine singular nominative: novi.

For example: nova stanarka = a new female tenant
novi stanari = new tenants

Here se is part of the verb useliti se, which means to move in. It is not translated word-for-word as himself in English here; it is simply part of the Serbian verb.

So you should learn this as a unit: useliti se = to move in

Without se, you would not have the same meaning.

Uselio is the masculine singular past form of the verb. In Serbian, past forms agree with the subject in gender and number.

Because stanar is masculine singular, the form is uselio.

Compare: on se uselio = he moved in
ona se uselila = she moved in
ono se uselilo = it moved in
oni su se uselili = they moved in

That is a very common learner question. In this kind of 3rd person singular reflexive past form, Serbian normally says uselio se, not je se uselio or se je uselio.

So the natural form is: Novi stanar se uselio sa porodicom.

Learners should treat se uselio as the normal pattern here. This is similar to other very common verbs: rodio se = was born
oženio se = got married
vratio se = returned

Because se is a clitic, and clitics in Serbian usually go in a fixed early position in the sentence, often after the first stressed element or phrase.

So the neutral word order is: Novi stanar se uselio sa porodicom.

Putting se later, such as Novi stanar uselio se..., sounds unnatural in normal standard usage.

Because useliti se specifically means to move into a place. The prefix u- gives the idea of into/in.

So: useliti se = move in
seliti se = move, relocate, be moving house in general

The sentence is about a completed move into a home/apartment, so uselio se is the right choice.

Yes.

useliti se focuses on moving into a home/apartment/building.
preseliti se means to move/relocate from one place to another more generally.
doseliti se means to move to a place, often from somewhere else, with focus on arrival.

So: uselio se = moved in
preselio se = moved/relocated
doselio se = moved here / moved to this place

Because sa means with, and it is used here to show accompaniment: the new tenant moved in with his family.

So: sa porodicom = with the family / with his family

Serbian often does not use possessives where English does. Depending on context, sa porodicom can naturally mean with his family.

Because the preposition s/sa meaning with requires the instrumental case.

The noun changes like this: porodica = family, nominative
porodicom = with the family, instrumental

So: sa porodicom = with the family

The ending -om is the normal instrumental singular ending for many feminine nouns of this type.

Yes, in many situations s and sa are just two forms of the same preposition. However, sa is often used for easier pronunciation, and it is the safer choice for learners.

In this sentence, sa porodicom sounds completely natural. S porodicom may also be heard, but sa porodicom is very common and comfortable in speech.

For a woman: Nova stanarka se uselila sa porodicom.

For several tenants: Novi stanari su se uselili sa porodicama.

Notice the changes: novi → nova for feminine singular
uselio → uselila for feminine singular
stanar → stanari for plural
In the plural, you also normally see the auxiliary su: su se uselili.