Jutro idę z nią do muzeum.

In Polish, the present tense of an imperfective verb is often used for a planned future action, especially when there is a time word like jutro.

So:

Jutro idę do muzeum = Tomorrow I’m going to the museum

This works much like English I’m going tomorrow.

Here, jutro makes the future meaning clear, so Polish does not need a special future form.

Because iść and chodzić do not mean exactly the same thing.

• iść / idę = to be going, to go in one specific direction / one specific trip
• chodzić / chodzę = to go regularly, habitually, or around on foot

So:

• Jutro idę do muzeum = Tomorrow I’m going to the museum (one planned trip)
• Chodzę do muzeum = I go to the museum / I go to museums regularly

A learner often wants to translate English go with one Polish verb, but Polish makes this distinction very clearly.

Yes, you could. Both are natural, but they feel a little different.

• Jutro idę z nią do muzeum = Tomorrow I’m going with her to the museum
  This often sounds like a plan or arrangement.
• Jutro pójdę z nią do muzeum = Tomorrow I’ll go with her to the museum
  This can sound a bit more like a decision, promise, or single completed action in the future.

Very roughly:

• idę = I’m going
• pójdę = I will go

Both are correct, but idę is extremely common for a planned near-future action.

Because after z meaning with, Polish uses the instrumental case.

The pronoun ona changes like this:

• ona = she
• nią = her

So:

• z nią = with her

You cannot say z ona.

This is one of the most important things to notice in Polish: words change their form depending on their role in the sentence.

The preposition z can mean different things depending on the case that follows it.

• z + instrumental = with
• z + genitive = from / out of

Here we have nią, which is the instrumental form, so:

• z nią = with her

Compare:

• Idę z nią. = I’m going with her.
• Wracam z muzeum. = I’m coming back from the museum.

So the case tells you the meaning.

Because Polish usually uses do + genitive to express movement to / into a place.

So:

• do muzeum = to the museum
• do szkoły = to school
• do domu = home / to the house

In this sentence, the speaker is moving toward the museum, so do is the normal choice.

Because w muzeum means in the museum, not to the museum.

Compare:

• Idę do muzeum. = I’m going to the museum.
• Jestem w muzeum. = I’m in the museum.

So:

• do = movement toward a place
• w = location inside a place

That is a very common Polish distinction.

Normally, do requires the genitive case, so learners often expect the noun to change.

But muzeum is one of those nouns whose singular form often looks the same in several cases. So even though the case is genitive here, the form is still muzeum.

That means:

• nominative: muzeum
• genitive after do: muzeum

So the grammar has changed, even if the spelling has not.

In Polish, the verb often already tells you who the subject is.

• idę = I am going / I go

Because of that, ja is usually unnecessary.

So:

• Jutro idę z nią do muzeum. = normal, natural
• Ja jutro idę z nią do muzeum. = possible, but more emphatic

You would use ja if you want contrast or emphasis, for example:

• Ja idę z nią, nie ty. = I’m going with her, not you.

Yes. Polish word order is fairly flexible.

This sentence can be rearranged in several ways, for example:

• Jutro idę z nią do muzeum.
• Idę jutro z nią do muzeum.
• Z nią idę jutro do muzeum.
• Do muzeum idę jutro z nią.

These versions are all possible, but they do not sound equally neutral. The original sentence is very natural and neutral.

Changing the word order usually changes emphasis, not the core meaning.

For example:

• Jutro at the beginning emphasizes when
• z nią earlier in the sentence can emphasize with whom
• do muzeum earlier can emphasize where

Usually, yes: iść basically refers to going on foot or to movement conceived in that way.

So literally, idę do muzeum suggests I’m walking to the museum.

In real life, though, people sometimes use it a bit more loosely in casual speech when the exact mode of transport is not the point.

If you specifically mean going by vehicle, Polish often uses jechać:

• Jutro jadę z nią do muzeum. = Tomorrow I’m going with her to the museum / I’m travelling there with her

So a learner should remember:

• iść = go on foot
• jechać = go by vehicle

Polish has no articles like a or the.

So muzeum can mean:

• a museum
• the museum

The exact meaning depends on context.

In this sentence, English normally says the museum, but Polish simply says muzeum.

That is completely normal.