После работы мы собираемся пойти в кино.

Because после requires the genitive case.

• работа = nominative, the dictionary form
• работы = genitive singular

So после работы literally means after work or after the workday.

This is a very common pattern:

• после урока = after the lesson
• после фильма = after the film
• после обеда = after lunch

In this sentence, после работы usually means after work, in the everyday sense of after finishing work / after the workday.

It does not usually sound like abstract work as a concept. It is more like:

• after work
• after we get off work
• once work is over

This expression is extremely common in Russian.

Here собираемся means are planning, are intending, or are getting ready to do something.

So:

• мы собираемся пойти в кино = we are planning to go to the movies

This is from the verb собираться. Depending on context, it can mean:

• to get together / gather
• to get ready
• to intend / plan

In this sentence, it clearly has the intend/plan meaning.

Russian often uses reflexive verbs in ways that do not translate literally into English.

The base verb собирать means to collect or to gather something.

But собираться can mean:

• to gather together
• to get ready
• to plan / intend

So in мы собираемся пойти в кино, the reflexive form is simply the normal dictionary form for this meaning. You should learn собираться + infinitive as a set pattern:

• Я собираюсь уйти. = I’m planning to leave.
• Мы собираемся поесть. = We’re going to eat / planning to eat.

Because пойти is the perfective verb, and here Russian prefers it to express a single planned action.

• идти = imperfective, to be going / to go on foot, process
• пойти = perfective, to set off / to go once

After собираться, Russian often uses the infinitive that matches the kind of action being planned. Since going to the movies is seen as one complete event, пойти sounds natural.

So:

• собираемся пойти = are planning to go

If you used идти, it would sound less standard here, or it would shift the nuance.

The difference is mainly aspect and viewpoint.

• идти в кино focuses more on the process or the idea of going
• пойти в кино focuses on the act of setting off or the event as a whole

Compare:

• Мы идём в кино. = We are going to the movies.
  This often means it is already happening now or is a current plan.

• Мы собираемся пойти в кино. = We are planning to go to the movies.
  This is about intention.

So in your sentence, пойти fits well because the action is still a plan and is viewed as one complete outing.

Both are possible, but they are not exactly the same in feel.

• в кино = to the movies / to see a movie
• в кинотеатр = to the movie theater / cinema building

В кино is the more natural idiomatic expression when talking about going to watch a film.

Compare:

• Мы идём в кино. = We’re going to the movies.
• Мы идём в кинотеатр. = We’re going to the cinema building / movie theater.

Also, кино is very often used in this set phrase and does not change form here.

Russian has no articles.

So Russian does not directly distinguish between:

• to a movie theater
• to the movie theater
• to the movies

The exact meaning is understood from context.

In в кино, the sense is idiomatic and usually means to the movies.

Yes, мы could be omitted, because the verb ending already shows the subject:

• собираемся = we are planning

So both are possible:

• Мы собираемся пойти в кино.
• Собираемся пойти в кино.

Including мы makes the subject explicit. It can sound a little clearer, more neutral, or slightly more emphatic depending on context.

Russian often drops subject pronouns when they are obvious.

Yes. Russian word order is flexible, although some versions sound more neutral than others.

The original sentence:

• После работы мы собираемся пойти в кино.

This is very natural and neutral: After work, we’re planning to go to the movies.

Other possible orders:

• Мы собираемся пойти в кино после работы.
• В кино мы собираемся пойти после работы.

These are all grammatical, but the emphasis changes:

• putting после работы first highlights the time
• putting в кино first highlights the destination/activity
• putting мы first can highlight the subject

So the original order is a very standard way to say it.

Yes:

• Мы собираемся пойти в кино после работы.

This is also completely natural.

The difference is mostly emphasis:

• После работы мы собираемся пойти в кино.
  starts with the time frame, like As for after work...

• Мы собираемся пойти в кино после работы.
  first gives the main statement, then adds after work

Both are fine.

It is often closer to we plan to, we intend to, or we’re getting ready to.

Depending on context, English might translate it as:

• we’re planning to go
• we intend to go
• we’re going to go

But be careful: English be going to is often just a future marker, while Russian собираться keeps a stronger sense of intention or preparation.

So мы собираемся пойти в кино is not just a plain future. It suggests a plan.

Yes. For example:

• После работы мы пойдём в кино.

That means After work we’ll go to the movies.

The difference is:

• мы собираемся пойти в кино = we are planning/intending to go
• мы пойдём в кино = we will go

The second version sounds more definite and straightforward. The original sentence focuses more on the fact that it is a plan.