Kad učiteljica govori brzo, teže ju razumijem.

Yes. Kad means when here, and it is basically the same as kada.

• kad = more common in everyday speech
• kada = a bit more formal or stylistically fuller

In this sentence, it introduces a time clause: when / whenever the teacher speaks quickly.

Because the sentence begins with a subordinate clause: Kad učiteljica govori brzo.

Croatian normally separates that kind of clause from the main clause with a comma:

• Kad učiteljica govori brzo, = subordinate clause
• teže ju razumijem. = main clause

This is very similar to English punctuation in sentences like When the teacher speaks quickly, I understand her less easily.

Yes. Učiteljica is a feminine noun and means female teacher.

• učitelj = male teacher
• učiteljica = female teacher

In this sentence, učiteljica is the subject, so it is in the nominative singular form.

Govori is the 3rd person singular present tense of govoriti (to speak).

It matches the subject učiteljica:

• ja govorim = I speak
• ti govoriš = you speak
• ona govori = she speaks

Since učiteljica is she, the verb form is govori.

Because brzo is an adverb, not an adjective.

Here it describes how she speaks:

• govori brzo = she speaks quickly

Compare:

• brza učiteljica = a fast teacher → brza is an adjective describing the noun
• učiteljica govori brzo = the teacher speaks quickly → brzo is an adverb describing the verb

Teže is the comparative form of the adverb teško.

• teško = with difficulty / difficultly
• teže = more difficultly / with more difficulty

So teže ju razumijem means I understand her with more difficulty or more naturally in English, I understand her less easily / it’s harder for me to understand her.

This works well because the sentence implies a comparison: when she speaks quickly, understanding her becomes more difficult than usual.

Ju means her.

It refers back to učiteljica. In this sentence, she is the person being understood, so Croatian uses a direct object pronoun:

• razumijem učiteljicu = I understand the teacher
• razumijem ju = I understand her

So ju is the feminine singular direct object pronoun here.

Both ju and je can be used as short forms meaning her in the accusative.

However, ju is often preferred for clarity, because je is also the very common form meaning is.

So in a sentence like this, ju makes it immediately clear that the word means her, not a form of to be.

Because ju is a clitic: a short, unstressed word that does not stand freely in the sentence the way English pronouns do.

In Croatian, clitics usually appear near the beginning of the clause, often in second position.

So:

• teže ju razumijem

is natural, because ju comes early in the clause.

English would place her after the verb: I understand her, but Croatian often places short object pronouns before the main verb.

It is not stated, because Croatian often leaves subject pronouns out when the verb already shows who the subject is.

Razumijem already means I understand.

So Croatian does not need ja unless you want emphasis or contrast.

• razumijem = I understand
• ja razumijem = I understand, with extra emphasis on I

Yes, to some extent. Croatian word order is more flexible than English word order.

For example, this is also natural:

• Kad učiteljica brzo govori, teže ju razumijem.

That version places brzo closer to govori, but the meaning stays the same.

What usually matters most is keeping clitics like ju in their normal position.

It can suggest either, depending on context.

In a sentence like this, it often has a general/habitual meaning:

• Whenever the teacher speaks quickly, I understand her less easily.

But it could also describe a specific situation:

• When the teacher speaks quickly, I understand her less easily.

Croatian often lets context decide between those two readings.