Upravo sada ne mogu naći ključ od stana.

Upravo sada means right now / this very moment and adds emphasis (like exactly now).
Sada is simply now and is more neutral. You can also hear sad(a) in speech:

• Upravo sada ne mogu… = right this second I can’t…
• Sada ne mogu… = I can’t now (could be “at the moment”)

Yes. Croatian commonly uses:

• ne mogu (I can’t) + infinitive (naći = to find)

So ne mogu naći literally maps to I can’t to-find, idiomatically I can’t find.

Mogu is the 1st person singular present form of moći (can / to be able to).
So ne mogu = I can’t / I’m not able to.

Full present (useful for reference):

• ja mogu
• ti možeš
• on/ona/ono može
• mi možemo
• vi možete
• oni/one/ona mogu

In standard Croatian, ne is usually written as a separate word with verbs:

• ne mogu, ne znam, ne radim

(There are a few special cases in the language historically, but for learners: treat ne + verb as two words.)

All are possible but with different nuance:

• naći = to find (simple, common)
• pronaći = to find / discover (often a bit more “formal” or “success after searching”)
• tražiti = to look for / search for (focus on the searching, not the result)

So:

• Ne mogu naći ključ. = I can’t find the key (result missing)
• Tražim ključ, ali ga ne mogu naći. = I’m looking for the key but I can’t find it.

Yes, naći is typically perfective (finding as a completed result). That fits well with “can’t find (achieve the result).”
An imperfective partner is often given as nalaziti (to be finding / to find repeatedly), but in everyday “I can’t find it (right now)” people still use naći very often.

Good catch: Croatian has a “genitive of negation” tendency, but in modern everyday Croatian accusative is very common, especially in sentences like this.

Here, ključ is accusative singular (direct object) and because it’s inanimate masculine, nominative = accusative (ključ).

You may encounter genitive in some contexts, styles, or set phrases, but Ne mogu naći ključ is the normal, natural choice.

Od requires the genitive case, so stan → stana (genitive singular).
ključ od stana literally means key of the apartment, i.e. the apartment key.

Yes, with slightly different feel:

• ključ od stana = most common everyday phrasing for “apartment key”
• ključ za stan = “a key for an apartment” (can sound more functional/purpose-based)
• ključ stana (genitive without od) = possible but more “compressed”/formal; many speakers prefer od in casual speech

No—stan means apartment/flat.
A “house” is usually kuća.
So ključ od stana = apartment key, not house key.

Word order is flexible, and moving elements changes emphasis:

• Neutral: Upravo sada ne mogu naći ključ od stana.
• Emphasize “the key”: Upravo sada ne mogu naći ključ od stana. (spoken stress) or Ključ od stana upravo sada ne mogu naći.
• Emphasize “right now”: Upravo sada ne mogu naći ključ od stana. / Ne mogu upravo sada naći ključ od stana. (less common but possible)

Yes. It would be ga (for ključ, masculine inanimate). Very natural:

• Upravo sada ga ne mogu naći. = Right now I can’t find it.
• Ne mogu ga naći. = I can’t find it.

Position note: object clitics like ga usually come early in the sentence (often after the first stressed element).