Nie otwieraj obu okien naraz, bo będzie przeciąg.

Otwieraj is the imperative form of otwierać, so it means open! when you are speaking to one person informally.

More exactly, it is:

• 2nd person singular
• informal: used with ty
• from the verb otwierać = to open

So Nie otwieraj... means Don’t open... when talking to one person.

This is about aspect, and it is a very common Polish pattern.

• otwierać = imperfective
• otworzyć = perfective

In affirmative commands, Polish often uses the perfective:

• Otwórz okno. = Open the window.

But in negative commands, Polish normally prefers the imperfective:

• Nie otwieraj okna. = Don’t open the window.

So Nie otwieraj obu okien naraz is the natural way to say it.
A form like Nie otwórz... would sound very unnatural in this context.

If you are speaking to more than one person, use:

• Nie otwierajcie obu okien naraz, bo będzie przeciąg.

If you want to be formal/polite to one person, use:

• Niech pan nie otwiera obu okien naraz, bo będzie przeciąg.
• Niech pani nie otwiera obu okien naraz, bo będzie przeciąg.

So the original otwieraj is only for one person informally.

Because the verb is negated by nie, and in standard Polish a direct object after a negated verb often appears in the genitive instead of the accusative.

Compare:

• Otwieraj oba okna. = affirmative
• Nie otwieraj obu okien. = negative

Here:

• oba okna = nominative/accusative form
• obu okien = genitive form

So the sentence changes case because of the negation.

Obu means both: the sentence is talking about the two specific windows in question.

So:

• obu okien = both windows
• dwóch okien = two windows

That difference matters:

• Nie otwieraj obu okien... = don’t open both of them
• Nie otwieraj dwóch okien... = don’t open two windows

Also, obydwu is a common longer variant of obu:

• Nie otwieraj obydwu okien...

That means basically the same thing.

Because okien is the genitive plural of okno.

The basic forms are:

• okno = window
• okna = windows
• okien = of windows / windows in genitive plural

Since obu is also in the genitive here, the whole phrase becomes:

• obu okien

So this is just normal case agreement inside the noun phrase.

Here naraz means at once, simultaneously, or all at once.

So:

• obu okien naraz = both windows at once

Yes, jednocześnie would give a very similar meaning:

• Nie otwieraj obu okien jednocześnie...

The difference is mostly style:

• naraz sounds very everyday and natural
• jednocześnie sounds a bit more neutral or formal

Also note the spelling: here it is naraz as one word.

Yes, it could be ponieważ, but bo is the normal everyday word for because.

Compare:

• ..., bo będzie przeciąg. = natural, common, conversational
• ..., ponieważ będzie przeciąg. = more formal/bookish

So bo is exactly what you would expect in ordinary speech.

Because the speaker is talking about the result of opening both windows.

• będzie przeciąg = there will be a draft
• jest przeciąg = there is a draft

So the idea is:

• Don’t open both windows at once, because then a draft will happen.

A very common alternative would be:

• ..., bo zrobi się przeciąg.

That also means because there’ll be a draft / because it’ll get drafty.

Because Polish has no articles like English a and the.

So przeciąg by itself can mean:

• a draft
• the draft

The context tells you which one makes sense.
In this sentence, English naturally uses a draft, but Polish just says przeciąg.

Also, after będzie, the noun is in the nominative:

• będzie przeciąg

Two words that learners often find difficult here are otwieraj and przeciąg.

Rough English-friendly approximations:

• otwieraj ≈ ot-VYE-rye
• przeciąg ≈ PSHE-chyongk

A few helpful notes:

• Polish stress is usually on the next-to-last syllable
• rz in przeciąg sounds like the zh sound in measure, but the cluster is harder because of the surrounding consonants
• ą in przeciąg is a nasal vowel; before the final consonant it sounds a bit like ong

So you can aim for something like:

• Nie otwieraj obu okien naraz, bo będzie przeciąg.
• roughly: Nye ot-VYE-rye OB-oo OH-kyen NA-raz, bo BEND-zhe PSHE-chyongk