Imamo pristup zadnjoj sobi.

A word-by-word breakdown is:

• Imamo = we have
• pristup = access
• zadnjoj = last / final, in a form that matches sobi
• sobi = room, in the dative singular

So the whole sentence means We have access to the last room.

Because Croatian often expresses that relationship through case, not with a preposition.

Here, pristup normally goes with the dative:

• pristup komu? čemu? = access to whom? to what?

So instead of a separate word meaning to, Croatian uses the dative form:

• zadnjoj sobi = to the last room

Because zadnja soba is the dictionary/basic form: the last room.

In this sentence, the noun phrase has to be in the dative singular because of pristup. So both words change:

• zadnja soba → nominative
• zadnjoj sobi → dative

The adjective has to agree with the noun in gender, number, and case, so both words change together.

It is dative singular feminine.

Why?

• soba is a feminine singular noun
• pristup requires the dative
• the adjective zadnja must match soba

So:

• soba → sobi
• zadnja → zadnjoj

That gives:

• zadnjoj sobi = to the last room

In Croatian, the verb ending already tells you who the subject is.

• imam = I have
• imaš = you have
• ima = he/she/it has
• imamo = we have

So mi is not necessary unless you want emphasis or contrast.

For example:

• Imamo pristup zadnjoj sobi. = neutral, normal
• Mi imamo pristup zadnjoj sobi. = We have access (maybe others do not)

Usually yes, but zadnji/zadnja/zadnje can sometimes mean either:

• last / final
• back / rear depending on context

So zadnja soba could mean:

• the last room in a sequence
• the back room

If you want a more clearly final/last meaning, Croatian also uses posljednja:

• Imamo pristup posljednjoj sobi.

In everyday speech, though, zadnja is very common.

Standard Croatian would normally use Imamo pristup zadnjoj sobi.

That is because pristup in this meaning goes with the dative without a preposition.

• zadnjoj sobi = correct with pristup

By contrast, u zadnju sobu means into the last room, and it is used with verbs of movement, such as:

• Idemo u zadnju sobu. = We are going into the last room.
• Možemo ući u zadnju sobu. = We can enter the last room.

So pristup and u + accusative are not used the same way.

Not exactly.

• Imamo pristup zadnjoj sobi = We have access to the last room
• Možemo ući u zadnju sobu = We can enter the last room

Imamo pristup often suggests:

• permission
• authorization
• availability of access
• possession of a key/card/code, etc.

It does not always focus on the physical act of entering. So the Croatian sentence is closer to have access than simply can go in.

Yes. Croatian word order is more flexible than English because case endings show grammatical relationships.

The most neutral version here is:

• Imamo pristup zadnjoj sobi.

But other orders are possible for emphasis, for example:

• Zadnjoj sobi imamo pristup. = emphasis on to the last room
• Pristup zadnjoj sobi imamo. = emphasis on access

Even though these are possible, the original order is the most natural and straightforward in ordinary speech.

Because Croatian does not have articles like English a/an/the.

So Croatian simply says:

• zadnja soba = a last room / the last room, depending on context
• zadnjoj sobi = to a last room / to the last room, depending on context

In this sentence, the meaning is naturally understood as the last room, especially because last usually points to a specific room.