Завтра мы собираемся заселиться в новую квартиру.

No. In this sentence, мы собираемся + infinitive means we are planning / intending / getting ready to do something.

So:

• мы собираемся заселиться = we’re going to move in / we’re planning to move in

The verb собираться can literally mean to gather in other contexts, but with an infinitive it often means to intend or to be about to do something.

Examples:

• Я собираюсь уйти. = I’m going to leave.
• Они собираются купить машину. = They’re planning to buy a car.

Заселиться means to move into a place and become settled there, especially a home, hotel room, dorm, apartment, etc.

In this sentence:

• заселиться в новую квартиру = to move into a new apartment

It is related to селиться (to settle/move in) with the prefix за-, which often gives the idea of beginning or completing the move-in.

This verb is commonly used for:

• apartments
• hotel rooms
• dorms
• houses

So the sentence sounds natural for moving into a new apartment.

The -ся ending makes the verb reflexive, but in Russian reflexive verbs do not always mean a literal English oneself action.

Here, заселиться is simply the normal dictionary form of this verb for move in / settle in. You do not usually translate the -ся separately.

Compare:

• селить = to settle someone in / house someone
• селиться = to settle in / move in oneself
• заселиться = to move in, check in, take up residence

So -ся helps show that the subject is the one entering and settling into the place.

Because it depends on собираемся.

In Russian, after собираться meaning to intend / plan, the next verb is normally in the infinitive:

• Мы собираемся заселиться...
• literally: We intend to move in...

This is the same pattern as:

• Я хочу поехать. = I want to go.
• Они решили остаться. = They decided to stay.

So собираемся is the main conjugated verb, and заселиться stays in the infinitive.

Because the sentence expresses movement into a place.

Russian uses:

• в + accusative for motion into
• в + prepositional for location in

Here there is movement:

• заселиться в новую квартиру = move into a new apartment

So:

• новая квартира = nominative
• в новую квартиру = accusative

Compare:

• Мы заходим в квартиру. = We are going into the apartment.
• Мы в квартире. = We are in the apartment.

Because after в you do not always use the same case.

With в:

• в + accusative = into, to, motion toward an enclosed space
• в + prepositional = in, inside, location

So:

• в новую квартиру = into a new apartment
• в новой квартире = in a new apartment

Since заселиться means moving into the apartment, Russian uses the accusative:

• квартиру, not квартире

Russian word order is much more flexible than English word order. Завтра is placed first here to set the time frame right away: Tomorrow...

The sentence could also be rearranged:

• Мы завтра собираемся заселиться в новую квартиру.
• Мы собираемся завтра заселиться в новую квартиру.

All of these are grammatical, but the emphasis changes slightly.

Starting with Завтра is very natural if the speaker wants to highlight when it will happen.

Yes, Russian often drops subject pronouns when they are clear from the verb form.

So both are possible:

• Завтра мы собираемся заселиться в новую квартиру.
• Завтра собираемся заселиться в новую квартиру.

Since собираемся clearly shows we, the pronoun is not strictly necessary.

However, мы may be included:

• for clarity
• for emphasis
• because the speaker wants to contrast we with someone else

Because собираться here is a present-tense verb meaning to plan / intend something that will happen later.

So the sentence literally works like:

• Tomorrow we are planning to move in...

Russian often uses present tense forms of verbs like собираться, хотеть, думать to talk about present intentions concerning the future.

The future meaning comes from:

• Завтра = tomorrow
• the meaning of собираемся = intend / are going to

Because the speaker is referring to a single completed event: moving in.

Russian aspect matters a lot:

• селиться / заселяться (imperfective) = to be moving in, to move in in a general/repeated/process sense
• заселиться (perfective) = to move in as one completed action

After собираться, Russian often uses a perfective infinitive when the plan is for one completed action:

• собираемся заселиться = we plan to move in

If you used an imperfective form, it would sound more like focusing on the process or habitual action, which is not the point here.

Yes, but the meaning would shift slightly.

Some related verbs:

• переехать в новую квартиру = to move to a new apartment
  This emphasizes changing residence.

• въехать в новую квартиру = to move into a new apartment
  This is also common and often focuses on entering the new place.

• заселиться в новую квартиру = to move in / settle into a new apartment
  This emphasizes taking up residence in the place.

So заселиться is very natural here, especially if the idea is we’ll be moving in and starting to live there.

Yes, it is natural and correct.

Завтра мы собираемся заселиться в новую квартиру. sounds like something a native speaker would say when talking about plans for the next day.

Depending on context, a native speaker might also say:

• Завтра мы переезжаем в новую квартиру.
• Завтра мы въезжаем в новую квартиру.

But the original sentence is fully natural and idiomatic.

A helpful stress guide is:

ЗАвтра мы́ собира́емся засели́ться в но́вую кварти́ру.

Approximate pronunciation:

• Завтра = ZAF-tra
• мы = my
• собираемся = sa-bee-RA-yem-sya
• заселиться = za-se-LEET-sa
• в новую = v NO-vu-yu
• квартиру = kvar-TEE-ru

Stress is important in Russian, especially in longer words like собираемся and заселиться.