Если уж мы всё равно едем в центр, то зайдём в книжный магазин.

Уж is a particle that adds emphasis. In this sentence it gives the feeling of since we're going there anyway or if we're already doing that.

It does not change the basic meaning of the sentence, but it makes the logic sound more natural and slightly more conversational. Without уж, the sentence is still correct; it just loses that extra shade of well, since that's the case....

They are similar in tone, but they do different jobs.

• всё равно means anyway / in any case
• уж adds emphasis, often with a sense of since that’s already true

So Если уж мы всё равно едем в центр... feels like:

• If we’re going to the center anyway, then...
• Since we’re going there anyway, then...

Using both together is very natural in spoken Russian and gives the sentence a slightly stronger might as well feeling.

Russian distinguishes between going on foot and going by transport.

• идти / идём = go on foot
• ехать / едем = go by vehicle or transport

So едем в центр suggests that the speakers are traveling to the city center by car, bus, metro, etc. If they were walking, Russian would normally use идём в центр instead.

Here едем is the imperfective verb ехать, and Russian often uses the present tense of an imperfective verb to talk about a planned or expected near-future action.

So мы едем в центр can mean:

• we are going to the center
• we’re heading to the center
• we’re going to be going to the center

Поедем would focus more on setting off or starting the trip. In this sentence, едем sounds more natural if the trip is already part of the plan, or is understood as something already decided.

Because this is motion toward a destination.

With verbs of motion:

• в + accusative = movement into / toward a place
• в + prepositional = location inside a place

So:

• едем в центр = we are going to the center
• находимся в центре = we are in the center

Here центр is in the accusative, but for this noun the accusative looks the same as the nominative: центр.

То is a correlative word often used in Russian conditional sentences after an если clause. It is similar to English then.

So the structure is:

• Если ... , то ... = If ... , then ...

In English, then is often omitted. In Russian, то is also optional in many cases, but it is very common and helps mark the result part of the sentence clearly.

Yes, absolutely.

You can say:

Если уж мы всё равно едем в центр, зайдём в книжный магазин.

That sounds natural too. Adding то just makes the conditional structure a little more explicit.

Зайдём comes from зайти, which often means drop by, stop in, or go into briefly/on the way.

That is exactly the idea here: while going to the center, the speakers will make a stop at the bookstore.

Compare:

• пойдём = we’ll go
• войдём = we’ll enter
• зайдём = we’ll drop in / stop by / pop into

So зайдём is the most natural choice if the visit is a convenient extra stop.

Because зайти в takes the accusative when it means movement into a place.

So:

• зайти в магазин = go into / stop by the store
• быть в магазине = be in the store

Again, this is the same movement-vs-location pattern:

• в + accusative for destination
• в + prepositional for location

Книжный магазин is masculine singular, and its accusative form is the same as the nominative: книжный магазин.

It is future.

Зайти is a perfective verb, and perfective verbs do not have a true present tense in Russian. Their present-looking forms actually refer to the future.

So:

• зайдём = we will drop in / we’ll stop by

That is why the sentence sounds like a completed future action: first they go to the center, then they stop by the bookstore.

Yes.

Russian uses a comma between the если clause and the main clause:

Если уж мы всё равно едем в центр, то зайдём в книжный магазин.

The comma is required whether то is present or not.

Yes, and that is very common.

• если уж = if, given that
• раз уж = since, seeing that, now that

Раз уж мы всё равно едем в центр, зайдём в книжный магазин sounds slightly less conditional and more like the fact is already accepted. It often feels very natural in everyday speech.

It is natural, neutral-to-colloquial everyday Russian.

Nothing in it is highly formal. The combination если уж and всё равно sounds like normal spoken reasoning: since we’re going there anyway, we might as well do this too.

So this is the kind of sentence you could easily hear in ordinary conversation.

Yes, Russian word order is flexible, though changes can shift emphasis a little.

For example, these are all possible:

• Если уж мы всё равно едем в центр, то зайдём в книжный магазин.
• Если мы всё равно едем в центр, то зайдём в книжный магазин.
• Раз уж мы едем в центр, зайдём в книжный магазин.

The original version sounds very natural and balanced. Moving words around usually changes what is emphasized, not the core meaning.