Musimy zdecydować dziś, czy jedziemy w góry, czy zostajemy nad morzem.

Because zdecydować is the perfective verb, meaning to make a decision / to decide once and complete it.

• musimy zdecydować = we have to decide
• musimy decydować would suggest we have to be deciding or we must make decisions repeatedly, which does not fit this sentence well.

In this sentence, the idea is about reaching one concrete decision: mountains or the seaside.

Yes, dziś can move around, because Polish word order is fairly flexible.

This sentence:

• Musimy zdecydować dziś, czy jedziemy w góry, czy zostajemy nad morzem.

could also be:

• Dziś musimy zdecydować, czy jedziemy w góry, czy zostajemy nad morzem.
• Musimy dziś zdecydować, czy jedziemy w góry, czy zostajemy nad morzem.

All are natural, but the emphasis changes slightly:

• Dziś musimy zdecydować... emphasizes today
• Musimy dziś zdecydować... sounds very neutral
• Musimy zdecydować dziś... can sound a bit more marked, as if stressing the timing at the end of that phrase

Because Polish often uses czy ... czy ... to mean whether ... or ....

So:

• czy jedziemy w góry, czy zostajemy nad morzem means
• whether we are going to the mountains or staying by the sea

The first czy introduces the indirect question (whether), and the second czy marks the alternative (or).

In English we usually do not repeat whether before the second option, but in Polish this repeated structure is very normal.

Polish very often uses the present tense to talk about a planned or expected future action, especially with imperfective verbs.

So:

• jedziemy w góry literally looks like we are going to the mountains
• zostajemy nad morzem literally looks like we stay by the sea

but in context they mean:

• we’re going / we’ll go to the mountains
• we’re staying / we’ll stay by the sea

This is extremely common in Polish.

These are two different prepositional patterns.

1. w góry

This means to the mountains, with movement toward a destination.

• w
  • accusative often expresses motion into/toward something
• góry here is the accusative plural form of góry

So:

• jedziemy w góry = we’re going to the mountains

2. nad morzem

This means by the sea / at the seaside

• nad
  • instrumental often expresses location by / near / over
• morzem is the instrumental singular of morze

So:

• zostajemy nad morzem = we’re staying by the sea

Polish uses different prepositions because the ideas are different:

• movement to a destination: w góry
• staying in a location: nad morzem

Because w góry expresses motion toward the mountains, so it takes the accusative.

Compare:

• jedziemy w góry = we’re going to the mountains
• jesteśmy w górach = we’re in the mountains

So:

• w
  • accusative = movement
• w
  • locative = location

That is why góry appears here, not górach.

Morzem is the instrumental singular of morze.

It appears after nad, because when nad describes location, it usually takes the instrumental:

• nad morzem = by the sea
• nad rzeką = by the river
• nad jeziorem = by the lake

If you were talking about motion toward such a place, Polish often uses a different structure, for example:

• jedziemy nad morze = we’re going to the seaside

So:

• nad morzem = location
• nad morze = direction

Yes, that is also correct.

This version uses perfective future forms:

• pojedziemy = we will go
• zostaniemy = we will stay

It sounds a bit more clearly future-oriented and slightly more definite.

Compare:

• czy jedziemy..., czy zostajemy...
  more like whether we’re going / whether we’re staying
• czy pojedziemy..., czy zostaniemy...
  more like whether we will go / whether we will stay

Both are natural. The original sentence sounds very conversational.

Almost none in meaning. Both mean today.

• dziś is a bit shorter and slightly more compact
• dzisiaj is equally common and natural

So you could also say:

• Musimy zdecydować dzisiaj, czy jedziemy w góry, czy zostajemy nad morzem.

This would mean the same thing.

Sometimes learners want to say something like:

• czy jedziemy w góry albo zostajemy nad morzem

But that is not the most natural structure here.

With indirect questions of this type, Polish normally uses:

• czy ..., czy ...

That is the standard pattern for whether ... or ...

Albo usually means or in ordinary coordination, but after the first czy, repeating czy is the natural choice.

Because Polish does not need it here.

After zdecydować, Polish can directly introduce the content of the decision with czy:

• Musimy zdecydować, czy... = We have to decide whether...

If the sentence were structured differently, Polish might use że for that, but not here. Since this is an indirect whether clause, czy is the correct word.

It can suggest both, depending on context.

Basic meaning:

• zostajemy nad morzem = we are staying by the sea / remaining at the seaside

Because zostawać / zostać often has the sense of remain / stay, it can imply:

• we are already there and not leaving, or
• the chosen holiday plan is to stay there rather than go somewhere else

In this sentence, it contrasts with jedziemy w góry, so the practical meaning is:

• Are we going to the mountains, or are we staying at the seaside?

Yes, but the structure changes slightly.

Original:

• Musimy zdecydować dziś, czy jedziemy w góry, czy zostajemy nad morzem.
• We have to decide today...

With trzeba:

• Trzeba dziś zdecydować, czy jedziemy w góry, czy zostajemy nad morzem.

This means:

• It’s necessary to decide today...

Difference:

• musimy explicitly means we must
• trzeba is more impersonal: it is necessary / one has to

Both are common and natural.

Yes, in standard Polish punctuation, the comma is needed here because czy jedziemy w góry, czy zostajemy nad morzem is a subordinate clause attached to the main clause:

• Musimy zdecydować dziś, czy jedziemy w góry, czy zostajemy nad morzem.

The second comma, before the second czy, is also standard because it separates the two alternatives inside that clause.

Polish punctuation is often stricter than English punctuation in sentences like this.