W bagażniku trzymamy małą torbę, wodę i koc na długą podróż.

Because w means in, and after w Polish usually uses the locative case when talking about location.

So:

• bagażnik = trunk / boot
• w bagażniku = in the trunk / in the boot

The ending changes from -ik to -iku because of the locative singular form.

Trzymamy is the 1st person plural present tense of trzymać.

It means we keep, we store, or sometimes we hold, depending on context.
In this sentence, we keep/store is the natural meaning:

• trzymamy = we keep / we store

Because Polish uses verb endings very clearly, the subject my (we) is not needed.

In Polish, subject pronouns are often left out because the verb ending already shows who is doing the action.

Here:

• trzymam = I keep
• trzymasz = you keep
• trzymamy = we keep

So trzymamy already means we keep, and adding my would usually only be for emphasis.

Because torba is the direct object of the verb trzymamy, so it has to be in the accusative case.

The noun and adjective both change:

• mała torba = a small bag (nominative)
• małą torbę = a small bag (accusative)

This is a very common pattern for feminine singular nouns:

• adjective -a → -ą
• noun -a → -ę

For the same reason: it is also a direct object, so it takes the accusative case.

• woda = water (nominative)
• wodę = water (accusative)

So in the list, both małą torbę and wodę are objects of trzymamy.

Because koc is a masculine inanimate noun, and in Polish the accusative singular of masculine inanimate nouns is usually the same as the nominative singular.

So:

• koc = blanket (nominative)
• koc = blanket (accusative)

That is why it does not visibly change.

Here na means something like for or for use on.

So:

• na długą podróż = for a long trip / for a long journey

After na, Polish often uses the accusative case, which is why:

• długa podróż = a long trip
• na długą podróż = for a long trip

This construction is very common when talking about purpose or intended use:

• kanapki na drogę = sandwiches for the road
• ubrania na zimę = clothes for winter

No, Polish word order is fairly flexible.

This sentence could also be:

• Trzymamy w bagażniku małą torbę, wodę i koc na długą podróż.

That would still mean basically the same thing. The version with W bagażniku at the beginning emphasizes the location a bit more, like In the trunk, we keep...

So the first position often highlights what the speaker wants to focus on.

Because Polish has no articles like English a/an/the.

So:

• torba can mean a bag or the bag
• bagażnik can mean a trunk or the trunk

You understand whether it is a or the from context.
In this sentence, English naturally translates it as the trunk and a small bag, but Polish does not mark that with separate words.

Most naturally, yes. In this sentence, w bagażniku clearly means in the car trunk or in the boot.

Depending on context, bagażnik can also refer to a luggage compartment or even a rack, but here the natural interpretation is the car’s storage space.

In normal understanding, it can be taken as the purpose of the whole set of items: a small bag, water, and a blanket for a long trip.

Because it comes right after koc, some people may feel it is most closely linked to koc, but in context it usually applies to all the things being kept in the trunk.

If someone wanted to make that connection even clearer, they could rephrase the sentence. But as it stands, the meaning is natural and understandable.