В лагере мы поставим палатку.

Because after в meaning in for a location, Russian uses the prepositional case.

• dictionary form: лагерь = camp
• prepositional singular: в лагере = in the camp

So here в лагере tells us where the action happens.

A useful contrast:

• в лагере = in the camp / at camp
• в лагерь = into the camp (motion toward it)

In this sentence, it is location, not movement, so в лагере is correct.

Because палатку is the accusative singular form of палатка.

• nominative: палатка = a tent
• accusative: палатку = a tent (as the direct object)

In мы поставим палатку, the tent is the thing being set up, so it is the direct object and must be in the accusative case.

This is very common with feminine nouns ending in -а:

• книга → книгу
• машина → машину
• палатка → палатку

Here поставим means we will put up / set up / pitch.

The verb is from поставить, which often means to place or to put, but with things like палатка it naturally means set up or pitch.

So:

• поставить палатку = to put up / pitch a tent

A very literal translation like we will place a tent is grammatically possible, but in normal English we will pitch a tent or we will put up a tent sounds much more natural.

Because поставим is the 1st person plural future form of the perfective verb поставить.

• я поставлю = I will set up
• мы поставим = we will set up

In Russian, perfective verbs form the future with simple endings like this, not with буду.

So:

• мы поставим палатку = we will set up a tent / we’ll pitch a tent

Because поставить is perfective, and it presents the action as a completed whole.

Here the idea is not just that the action will be in progress, but that we will get the tent set up.

Compare:

• мы поставим палатку = we will set up the tent / we’ll get it pitched
  
  • focus on the completed result
• мы будем ставить палатку = we will be setting up the tent
  
  • focus on the process
• мы ставим палатку = we are setting up a tent / we set up a tent
  
  • depending on context

So поставим is the natural choice if the speaker means a single future action with a clear result.

Yes. Russian often omits subject pronouns when the verb ending already shows who is doing the action.

Since поставим already means we will set up, the sentence could also be:

• В лагере поставим палатку.

Including мы can add a little emphasis, contrast, or clarity:

• В лагере мы поставим палатку, а не домик.
• Мы can also simply sound natural in context if the speaker wants to mention the subject explicitly.

So мы is correct, but not always necessary.

No. Russian word order is fairly flexible, because the case endings show each word’s role.

The neutral version here is:

• В лагере мы поставим палатку.

But other orders are also possible:

• Мы поставим палатку в лагере.
• Палатку мы поставим в лагере.
• В лагере палатку мы поставим.

The basic meaning stays similar, but the emphasis changes:

• putting в лагере first highlights the setting
• putting палатку first highlights the object
• putting мы first highlights who will do it

So word order in Russian often reflects focus more than strict grammar.

A good stress pattern is:

В ла́гере мы поста́вим пала́тку.

Word by word:

• в
• ла́гере
• мы
• поста́вим
• пала́тку

The main stressed syllables are:

• ла́- in ла́гере
• -ста́- in поста́вим
• ла́- in пала́тку

That stress is important, especially in longer Russian words.

It can mean either, depending on the context and how naturally you want to say it in English.

Literally, it is in the camp, but in many situations English would say:

• at camp
• at the campsite
• in camp

If the sentence is about a camping trip, at the campsite or at camp may sound more natural in English. But grammatically, the Russian phrase is simply в лагере.