На следующей остановке нам нужно пересесть на трамвай, иначе мы не успеем.

Because остановка here means a stop as a point on a route, and Russian normally says на остановке for at the stop.

So:

• на остановке = at the stop
• на следующей остановке = at the next stop

This is just the usual preposition with this noun. Using в would sound wrong here.

Also, следующей остановке is in the prepositional case because it follows на in a location meaning:

• следующая остановка → nominative
• на следующей остановке → prepositional

Because it agrees with остановке, which is:

• feminine
• singular
• prepositional case

The base form is следующая остановка = the next stop.

After на in a location sense, both words change:

• следующая остановка
• на следующей остановке

So следующей is simply the correct feminine singular prepositional form of следующий.

Both can often be translated as we need to / we must, but they are not exactly the same.

нам нужно + infinitive

This is a very common Russian structure meaning:

• we need to
• it is necessary for us to

Literally, it works more like:

• to us, it is necessary to...

That is why нам is in the dative, not мы.

мы должны

This usually sounds more like:

• we are obliged to
• we must
• we are supposed to

In this sentence, нам нужно пересесть sounds natural and practical: it is what is necessary in order to get somewhere on time.

So:

• нам нужно пересесть = we need to transfer
• мы должны пересесть = we must transfer / we are required to transfer

Нужно is an impersonal predicate word meaning necessary / needed.

In sentences like this, Russian often uses:

• мне нужно... = I need to...
• тебе нужно... = you need to...
• нам нужно... = we need to...

So in нам нужно пересесть, the idea is:

• it is necessary for us to transfer

A useful point: нужно does not change for person or number here.

Compare:

• Мне нужно идти
• Ему нужно идти
• Нам нужно идти

It stays нужно every time.

Пересесть is the perfective verb meaning to transfer / change to another vehicle / move over and sit somewhere else.

Here it means to transfer from one form of transport to another.

Why perfective? Because this is a single completed action:

• at the next stop,
• we need to transfer,
• and then continue the trip.

Russian uses perfective here because the transfer is seen as one complete event.

Compare:

• пересесть = to transfer once, successfully
• пересаживаться = to be transferring / to transfer habitually / repeatedly

In this sentence, the one-time completed action is what matters, so пересесть is the natural choice.

With verbs of boarding or changing to transport, Russian often uses на + accusative.

So:

• сесть на трамвай = get on a tram
• пересесть на трамвай = transfer to a tram

That is why you see:

• на трамвай, not на трамвае

Here трамвай is in the accusative, but for this masculine inanimate noun, the accusative form looks the same as the nominative:

• трамвай = nominative
• трамвай = accusative

So the form does not visibly change, but the case is still accusative.

Specifically transfer to a tram.

The prefix пере- adds the idea of changing over from one thing to another.

So:

• сесть на трамвай = get on a tram
• пересесть на трамвай = change/transfer to a tram

This strongly suggests that the speakers are already using some other form of transport and need to switch.

Иначе means otherwise or or else.

In this sentence:

• ..., иначе мы не успеем. = ..., otherwise we won’t make it / otherwise we won’t be on time.

It often introduces the consequence of not doing what was just mentioned.

Examples:

• Поторопись, иначе опоздаешь. = Hurry up, otherwise you’ll be late.
• Нам нужно пересесть на трамвай, иначе мы не успеем.

It is very natural in this position, after a comma.

Because успеем is perfective future, and that fits the meaning here.

The verb is:

• успеть = to manage to do something in time / to make it in time

So:

• мы не успеем = we won’t make it in time

This sentence is about a future result:

• if we do not transfer at the next stop,
• then later we will fail to arrive/do something in time.

That is why Russian uses the future form успеем.

By contrast:

• мы не успеваем usually means we are not making it / we are running out of time right now, as a present situation.

Not exactly. Успеть means to manage to do something in time.

It is often followed by an implied or explicit goal.

So мы не успеем can mean:

• we won’t make it in time
• we won’t manage to get there in time
• we won’t be in time

It is a very common Russian verb for situations involving time pressure.

Compare:

• Я успел на поезд. = I made the train.
• Мы не успеем. = We won’t make it.

So it is broader than just to be punctual.

Yes. Нам надо пересесть на трамвай... would also be natural.

In many everyday contexts, надо and нужно are very close:

• надо = need to, have to
• нужно = need to, necessary to

Very roughly:

• надо can sound a bit more conversational
• нужно can sound a bit more neutral or slightly more formal

But in this sentence, both work well.

Yes, fairly flexible. Russian word order can change for emphasis.

The original:

• На следующей остановке нам нужно пересесть на трамвай, иначе мы не успеем.

This is natural because it starts with the time/place point:

• at the next stop

Other possible versions:

• Нам нужно пересесть на трамвай на следующей остановке, иначе мы не успеем.
• Иначе мы не успеем, на следующей остановке нам нужно пересесть на трамвай.
  This is possible, but the emphasis changes and it sounds less neutral.

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

A very natural spoken variant would be:

• На следующей остановке нам надо пересесть на трамвай, иначе не успеем.

What changed?

1. надо instead of нужно
   Slightly more conversational.

2. Dropping мы in иначе не успеем
   Russian often omits subject pronouns when they are obvious from the verb form.

So не успеем already clearly means we won’t make it, and мы is not required.