Danas ostajem u uredu dulje zbog projekta.

Croatian often uses the present tense to talk about planned or expected near-future actions, especially with a time word like danas (today).
So Danas ostajem... is a natural way to say I’m staying today / I’ll be staying today.
You could also say Danas ću ostati... (future with ću) but it can feel a bit more explicit/marked.

They come from different aspect pairs:

• ostajati / ostajem = imperfective (focus on the process/duration: staying, remaining)
• ostati / ostanem = perfective (focus on the one-time result: to stay/remain (and that’s it))

In this sentence, ostajem ... dulje fits the idea of staying for a longer time (duration), so the imperfective ostajem is very typical.

Because u changes meaning depending on the case:

• u + locative = location (in/at): u uredu = in/at the office
• u + accusative = movement into: u ured = into the office

Here you’re already there and staying, so it’s u uredu (locative).

uredu is locative singular of ured (office, masculine).
Many masculine nouns take -u in the locative singular: ured → (u) uredu.

It can mean either, depending on context. Croatian u + locative often covers both English in and at for places like offices, schools, etc. If you need to be more specific, context usually does the job rather than changing the grammar.

dulje means longer (more time). It’s the comparative adverb from dugo (for a long time).
If you mean later (in the day), you’d usually say kasnije:

• Ostajem dulje. = I’m staying longer (than usual / than expected).
• Ostajem kasnije. = I’m staying later (leaving later).

Because you’re comparing the duration to a normal/expected baseline:

• dugo = long (no comparison): I’m staying a long time.
• dulje = longer (comparison implied): I’m staying longer (than usual/than you/than planned).
  Even if the comparison isn’t stated, it’s understood.

Yes, in everyday speech dulje and duže are often interchangeable and mean longer.
dulje is commonly considered more standard in some contexts, while duže is also very widespread (regional preferences exist).

The preposition zbog (because of) requires the genitive case.
So projekt (nominative) becomes projekta (genitive): zbog projekta = because of the project.

Often yes, in nuance:

• zbog is very common and neutral, but it can sometimes suggest cause/blame depending on context.
• radi often sounds more like purpose/intent (for the sake of, due to in a more goal-oriented sense).

In many everyday sentences they can both work, but zbog projekta is perfectly natural.

Croatian typically drops subject pronouns because the verb ending already shows the subject:

• ostajem = I stay / I’m staying

You’d add ja mainly for emphasis or contrast:

• Danas ja ostajem u uredu... = I (not someone else) am staying...

Yes—Croatian word order is flexible, and changes mostly affect emphasis. For example:

• Danas ostajem u uredu dulje zbog projekta. (neutral)
• U uredu ostajem danas dulje zbog projekta. (emphasizes at the office)
• Zbog projekta danas ostajem u uredu dulje. (emphasizes the reason)