Wyjmij proszę butelkę z torby i daj mi jeden łyk wody.

They are imperative forms, used to tell someone to do something.

• wyjmij = take out
• daj = give

More specifically, these are 2nd person singular imperatives, so they are used when speaking to one person in the ty form.

The dictionary forms are:

• wyjąć → wyjmij
• dać → daj

Both verbs here are also perfective, which means the speaker is asking for a completed action: take the bottle out, then give me a sip.

proszę means please here. It softens the command and makes it more polite.

So:

• Wyjmij butelkę... = Take out the bottle...
• Wyjmij proszę butelkę... = Please take out the bottle...

In Polish, proszę is quite flexible in position. You could also hear:

• Proszę, wyjmij butelkę...
• Wyjmij butelkę, proszę...

All are natural, though the exact tone may vary slightly.

Because butelkę is the accusative singular form of butelka.

Here, butelka is the direct object of wyjmij: it is the thing being taken out. In Polish, direct objects often go into the accusative case.

So:

• butelka = bottle (dictionary form, nominative)
• butelkę = bottle (accusative singular)

This is a very common pattern for feminine nouns ending in -a:

• torba → torbę
• książka → książkę
• butelka → butelkę

Because the preposition z in the sense of from / out of requires the genitive case.

So:

• torba = bag
• z torby = from the bag / out of the bag

This is one of the things Polish learners have to memorize: many prepositions require a specific case.

Here:

• z + genitive = from, out of

Examples:

• z domu = out of the house
• z pudełka = out of the box
• z torby = out of the bag

Both forms can mean me, but they are used differently.

• mi = the usual unstressed dative form
• mnie = the stressed form, used for emphasis, contrast, or after some prepositions

In daj mi..., mi is the normal choice because it is short and unstressed:

• Daj mi łyk wody. = Give me a sip of water.

You might use mnie if you want contrast or emphasis:

• Daj mnie, nie jemu.
  Better naturally: Daj mnie? No — this is actually wrong, because dać takes dative, so it would be:
  Daj mnie...? not correct.
  The proper contrast would be: Daj mnie? No.

  The correct contrastive example is:

• Daj mnie? still wrong.
• Daj mnie...? no, because mnie here is not dative.

So the important thing is:

• dać komuś = to give to someone
• Therefore you need the dative
• The usual short dative form is mi
• The full dative form is mnie, but it is used mainly when stressed: Daj mnie trochę, a nie jemu is still not natural with dać, so a better example with dative emphasis is: Mnie daj wodę, nie jemu.

In this sentence, mi is simply the normal natural choice.

Good question. The phrase jeden łyk wody is the direct object of daj, so it is indeed in the accusative.

But łyk is a masculine inanimate noun, and in the singular, the accusative often looks exactly the same as the nominative.

So:

• nominative: jeden łyk
• accusative: jeden łyk

They look identical, but grammatically this is still the object form.

This is very common with masculine inanimate nouns in Polish.

Because after a noun like łyk meaning sip, Polish usually uses the genitive for the substance or thing being measured.

So:

• łyk wody = a sip of water
• literally: a sip of water

This is similar to other expressions:

• szklanka wody = a glass of water
• kawałek chleba = a piece of bread
• butelka mleka = a bottle of milk

So in jeden łyk wody:

• łyk is the main noun
• wody is in the genitive because it means of water

Yes, absolutely. Daj mi łyk wody is very natural.

Adding jeden can do a few things:

• make the request feel a little more specific
• emphasize just one sip
• make the phrase sound a bit fuller in some contexts

So both are correct:

• Daj mi łyk wody.
• Daj mi jeden łyk wody.

The version without jeden is probably more common in everyday speech unless you specifically want to stress one.

It is addressed to one person using the ty form, so grammatically it is informal singular.

• wyjmij
• daj

These are forms you use with someone you address as ty.

However, the sentence includes proszę, which makes it sound more polite. So the tone is:

• informal grammar
• but polite wording

A more formal version could be something like:

• Proszę wyjąć butelkę z torby i dać mi łyk wody.
• Niech pan/pani wyjmie butelkę z torby i da mi łyk wody.

Because the speaker wants single completed actions.

• wyjąć / wyjmij = take out, successfully remove
• dać / daj = give, complete the act of giving

This fits the situation well: first take the bottle out, then give me a sip.

If you used imperfective forms, the meaning or tone would change:

• wyjmuj can sound like be taking out, take out repeatedly, or sometimes a rougher command depending on context
• dawaj can mean give in colloquial speech, but it can also sound more pushy, impatient, or ongoing

So in this sentence, the perfective imperatives are the most natural choice.

Polish word order is more flexible than English word order, because case endings show the grammatical roles.

The given order is very natural:

• Wyjmij proszę butelkę z torby i daj mi jeden łyk wody.

But some variation is possible, for example:

• Proszę, wyjmij butelkę z torby i daj mi łyk wody.
• Wyjmij butelkę z torby i daj mi łyk wody, proszę.

The exact order can affect tone, emphasis, or style, but the core meaning stays the same.

That said, not every reshuffling sounds equally natural, so learners should usually start by copying common patterns like the original sentence.