Learn Hardcore Croatian: On ljubazno pita učiteljicu za pomoć.

Nominative (dictionary form, subject): učiteljica – the teacher (she) teaches.
Accusative (direct object): učiteljicu – He asks *the teacher.*

Croatian changes the ending of nouns to show their grammatical role:

učiteljica → učiteljicu (feminine, -a noun, accusative singular)

So in On ljubazno pita učiteljicu za pomoć, the person being asked is the object, so you must use učiteljicu, not učiteljica.

What does On add here? Can I drop the subject pronoun in Croatian?

On means he, and it is the subject in the nominative case.

In Croatian, subject pronouns (ja, ti, on, ona, mi, vi, oni...) are often omitted, because the verb ending already shows the person:

Pita učiteljicu za pomoć. = He/She is asking the teacher for help.
On pita učiteljicu za pomoć. = He is asking the teacher for help (explicit, maybe contrasting with someone else).

You usually:

Omit on in neutral, context-clear sentences.
Use on for emphasis or contrast (e.g. On pita, a ona šuti. – He is asking, and she is silent.)

So yes, you can absolutely say:

Ljubazno pita učiteljicu za pomoć.

How is ljubazno formed, and what exactly does it mean compared to English kindly or politely?

Ljubazno is an adverb formed from the adjective ljubazan (kind, polite):

ljubazan (m.) / ljubazna (f.) / ljubazno (n.) – kind, polite
ljubazno (adverb) – kindly, politely

Formation:
Adjective stem ljubazan → adverb ljubazno (with the -no ending), similar to English kind → kindly.

Meaning in this sentence:

On ljubazno pita učiteljicu za pomoć.
= He politely asks the teacher for help.
(not rude, not demanding; he asks in a considerate way)

Depending on context, ljubazno is usually closer to politely than to kindly.

Where can ljubazno go in the sentence? Is the word order fixed?

The word order in Croatian is fairly flexible, especially for adverbs like ljubazno. All of these are grammatically possible:

On ljubazno pita učiteljicu za pomoć. (neutral, very natural)
On pita učiteljicu ljubazno za pomoć. (less common; puts slight emphasis on ljubazno)
On pita učiteljicu za pomoć ljubazno. (emphasis at the end, a bit marked)

General rules:

The most neutral position for manner adverbs (how? politely, quickly, etc.) is just before the verb:
- On ljubazno pita...
Moving ljubazno towards the end gives it more emphasis in speech.

So the given sentence has the most typical and neutral word order.

Why do we say pita učiteljicu za pomoć and not just pita učiteljicu pomoć?

Croatian uses different patterns with the verb pitati (to ask), depending on what you are asking:

ask someone something (a question, information)
- Pattern: pitati nekoga nešto (two accusatives)
- Example:
  - Pitam učiteljicu lekciju.
    (I ask the teacher about the lesson. – literally ask the teacher the lesson)
ask someone for something (a favor, help)
- Pattern: pitati (or moliti) nekoga za nešto
- Example:
  - Pita učiteljicu za pomoć.
    (He asks the teacher for help.)

So:

pita učiteljicu pomoć ❌ – ungrammatical.
pita učiteljicu za pomoć ✅ – correct: asks the teacher for help.

The preposition za is needed to show that this is a request for something, not just a question about something.

What case is pomoć in, and does it change form after za?

After za, the noun is in the accusative case.

The noun pomoć (help) is feminine.
Nominative singular: pomoć
Accusative singular: pomoć (same form)

So in za pomoć, pomoć is accusative singular, but it looks the same as the nominative. This is normal for many feminine nouns that end in a consonant.

Rule:
za + accusative → za pomoć, za njega, za sutra, za mene, etc.

What is the infinitive and full present-tense conjugation of pita?

The infinitive is pitati – to ask.

Present tense of pitati:

ja pitam – I ask / am asking
ti pitaš – you ask / are asking (singular, informal)
on / ona / ono pita – he / she / it asks / is asking
mi pitamo – we ask / are asking
vi pitate – you ask / are asking (plural or formal)
oni / one / ona pitaju – they ask / are asking

In the sentence On ljubazno pita učiteljicu za pomoć, pita is 3rd person singular present.

Does pita mean asks or is asking? How do you express continuous vs habitual actions in Croatian?

Pita can mean both:

He asks (habitual, general)
He is asking (right now)

Croatian present tense usually covers both the simple and continuous English presents. Context decides:

Svaki dan pita učiteljicu za pomoć.
= He asks the teacher for help every day. (habitual)
Sada pita učiteljicu za pomoć.
= He is asking the teacher for help now. (currently)

You don’t normally need a special continuous form. You simply add a time expression like sada, trenutno, uvijek, često if you want to clarify.

Does učiteljicu specifically mean a female teacher? How would I talk about a male teacher?

Yes. Učiteljica is a female teacher, so učiteljicu is “(the) female teacher” in the accusative.

For a male teacher:

Nominative: učitelj – male teacher
Accusative: učitelja

So you would say:

On ljubazno pita učitelja za pomoć.
= He politely asks the (male) teacher for help.

Other common words:

nastavnik / nastavnica – usually for primary/lower secondary classes
profesor / profesorica – usually for high school and university

But in your sentence, učiteljicu clearly refers to a female teacher.

How would I say He politely asked the teacher for help in the past tense?

Use the perfect tense:

On je ljubazno pitao učiteljicu za pomoć.
= He politely asked the teacher (female) for help.

Notes:

je – auxiliary (3rd person singular of biti, to be)
pitao – past participle (masculine singular) of pitati

If the subject were female:

Ona je ljubazno pitala učiteljicu za pomoć.

Many speakers might actually prefer zamolio (asked/begged politely) for “asked for help”:

On je ljubazno zamolio učiteljicu za pomoć.
(very natural for He politely asked the teacher for help.)

Croatian has no words for a or the. How do you know it’s the teacher and not a teacher here?

Croatian does not have articles like a/an or the. The noun učiteljicu by itself can mean:

the teacher
a teacher

Which one you choose in English depends on context:

If you already know which teacher you are talking about, you translate as the teacher.
If she is mentioned for the first time, you might say a teacher.

Croatian relies on:

context,
word order,
pronouns or demonstratives (tu učiteljicu, tu jednu učiteljicu, tu našu učiteljicu, etc.)

to express what English would show with a/the.

Is On ljubazno pita učiteljicu za pomoć a naturally polite way to ask in Croatian, or would native speakers say something else?

As a description, it is completely natural:

On ljubazno pita učiteljicu za pomoć.
= He is politely asking the teacher for help.

But as an actual request spoken to the teacher, native speakers would usually use different forms, for example:

Učiteljice, možete li mi pomoći? – Teacher, can you help me?
Molim vas, možete li mi pomoći? – Please, can you help me?
Ljubazno vas molim za pomoć. – I kindly/politely ask for your help. (formal, written)

So your sentence is good as a narration or example of grammar, and it clearly shows polite intent, but real-life requests are usually phrased with molim, moliti, moći, and sometimes ljubazno in more formal styles.