Cijelo jutro učim hrvatski.

Because Croatian often drops subject pronouns when they are not needed. The verb form already tells you who the subject is.

• učim = I learn / I study

So Cijelo jutro učim hrvatski. already clearly means I am studying Croatian all morning / I’ve been studying Croatian all morning.

You can add ja if you want emphasis or contrast:

• Ja učim hrvatski, a on uči njemački.
  I study Croatian, and he studies German.

Učim is the 1st person singular present tense of the verb učiti, which means to learn or to study.

So:

• učiti = to learn / to study
• učim = I learn / I am learning / I study / I am studying

Croatian present tense is often broader than English, so one form can match several English possibilities depending on context.

Because Croatian does not use a special tense like the English present perfect continuous. It often just uses the present tense for an action that is still going on.

With cijelo jutro (all morning), the sentence strongly suggests an activity that started earlier and continues up to now.

So natural English translations include:

• I’ve been studying Croatian all morning.
• I’m studying Croatian all morning. (less natural in English)
• I’ve studied Croatian all morning. (possible, but usually less natural than I’ve been studying)

In other words, Croatian uses učim, while English often prefers have been studying here.

Cijelo jutro means all morning or the whole morning.

Grammatically, this is an example of the accusative of duration: Croatian can use the accusative case to express how long something lasts, often without a preposition.

So:

• Cijelo jutro učim hrvatski. = I’ve been studying Croatian all morning.
• literally: Whole morning I study Croatian.

Also, jutro is a neuter noun, and in the singular its nominative and accusative forms are the same:

• nominative: jutro
• accusative: jutro

That is why you do not see a change in the noun itself.

Because cijelo must agree with jutro in gender, number, and case.

• jutro is neuter singular
• here it is in the accusative singular
• so the adjective must also be neuter singular accusative

That gives:

• cijelo jutro = the whole morning / all morning

Compare:

• cijeli dan = the whole day (dan is masculine)
• cijela noć = the whole night (noć is feminine)
• cijelo jutro = the whole morning (jutro is neuter)

Because in everyday Croatian, the word jezik (language) is often simply left out when the meaning is obvious.

So:

• učim hrvatski = I study Croatian
• full version: učim hrvatski jezik = I study the Croatian language

The short version is very common and natural.

A useful detail: hrvatski stays in the masculine form here because it originally agrees with the omitted noun jezik, which is masculine:

• hrvatski jezik
• učim hrvatski (jezik)

That is why it is hrvatski, not hrvatsko.

It can mean both, depending on context.

With languages, učiti often covers both ideas:

• to study Croatian
• to learn Croatian

In many real situations, English speakers might choose study when talking about the activity itself, and learn when focusing on the goal. Croatian often just uses učiti for both.

So in this sentence, both are possible:

• I’ve been studying Croatian all morning.
• I’ve been learning Croatian all morning.

The first is often the more natural English translation.

Croatian word order is fairly flexible, although some orders sound more neutral than others.

Your sentence:

• Cijelo jutro učim hrvatski.

is perfectly natural and puts all morning near the front for emphasis on duration.

Other possible orders:

• Učim hrvatski cijelo jutro.
• Hrvatski učim cijelo jutro.

These are also possible, but they may shift the emphasis slightly.

Very roughly:

• Cijelo jutro učim hrvatski. → emphasis on all morning
• Učim hrvatski cijelo jutro. → more neutral in some contexts
• Hrvatski učim cijelo jutro. → emphasis on Croatian

So yes, the order can change, but the original sentence is a very natural one.

It means for the whole of this morning or all morning in a specific situation, not every morning.

If you want every morning, Croatian would usually say:

• Svako jutro učim hrvatski. = I study Croatian every morning.

So the difference is:

• Cijelo jutro učim hrvatski. = I’ve been studying Croatian all morning.
• Svako jutro učim hrvatski. = I study Croatian every morning.

Because učiti is imperfective, and that fits an ongoing activity.

• učiti = to study / to be learning
• naučiti = to learn, in the sense of manage to learn / master

In this sentence, the speaker is describing a process in progress over a period of time:

• Cijelo jutro učim hrvatski.

That is exactly the kind of situation where Croatian normally uses the imperfective verb.

If you used naučiti, the meaning would change toward finishing or successfully learning something, not simply spending time studying it.

So:

• učim hrvatski = I’m studying / learning Croatian
• naučio sam hrvatski = I learned Croatian / I have mastered Croatian

For this sentence, učim is the natural choice.