Nikad ne kasnim u školu.

Croatian requires negative concord: a negative word like nikad (never) must be accompanied by the negative particle ne before the verb. This is normal and not “double negative” in the English sense.

• Correct: Nikad ne kasnim.
• Also: Nitko ne dolazi (Nobody is coming), Ništa ne razumijem (I don’t understand anything). Leaving out ne with nikad in a full sentence is ungrammatical.

Yes. Nikad and nikada mean the same thing. Nikada can feel a bit more emphatic or formal, but both are fully standard:

• Nikad ne kasnim u školu.
• Nikada ne kasnim u školu.

Typical placements:

• At the start: Nikad ne kasnim u školu. (neutral and common)
• Before the verb inside the clause: Ja nikad ne kasnim u školu. You cannot move ne away from the verb; it must stay immediately before it: ne kasnim.

No. The verb ending already encodes the subject. Kasnim means “I am late.”
Add ja only for emphasis or contrast:

• Neutral: Nikad ne kasnim u školu.
• Emphatic: Ja nikad ne kasnim u školu.

Because u with the accusative (u školu) expresses motion or destination, matching the idea “late to school.”
Use the locative (u školi) for location “at/in school.”

• Going/arriving: Idem u školu. Kasnim u školu.
• Being there: Ja sam u školi.

With škola, Croatian uses u for both “to school” (u školu) and “at school” (u školi). Na školu is not used in this sense.
However, other nouns do take na:

• To work: na posao; at work: na poslu
• To university: very commonly na fakultet; at university: na fakultetu
• To an event: na koncert, na sastanak

Školu is accusative singular of the feminine noun škola. It’s required by the preposition u when expressing motion toward a place. Mini-paradigm:

• Nominative: škola
• Genitive: škole
• Dative: školi
• Accusative: školu
• Locative: školi
• Instrumental: školom

Kasniti means “to be late.” Present tense:

• ja kasnim
• ti kasniš
• on/ona/ono kasni
• mi kasnimo
• vi kasnite
• oni/one/ona kasne It’s imperfective, so it’s good for habits and ongoing situations.

Use the perfective in the past:

• Male speaker: Nikad nisam zakasnio u školu.
• Female speaker: Nikad nisam zakasnila u školu. Using nikada is equally fine: Nikada nisam zakasnio/zakasnila u školu.
  You may also hear the imperfective past (nisam kasnio/la), but perfective zakasniti is more natural for “ever/never” experiences.

Because za is not used with kasniti to mean “late for” a destination or event. Use:

• kasniti u
  • accusative for enclosed places: kasnim u školu, kasnim u razred
• kasniti na
  • accusative for events/meetings/transport: kasnim na sastanak, kasnim na autobus So, not kasnim za školu.

Use ikad (ever), not nikad:

• Neutral present: Kasniš li ikad u školu?
• For a life experience: Jesi li ikad zakasnio u školu? (male) / Jesi li ikad zakasnila u školu? (female)