Én magyarul tanulok.

Yes. Hungarian usually leaves out the subject pronoun when it is clear from the verb ending.

So:

• tanulok already means I learn / I am studying
• Én tanulok means I learn / I am studying, but with extra emphasis on I

In this sentence, Én can sound contrastive or slightly emphatic, like:

• I’m the one learning Hungarian.
• As for me, I’m learning Hungarian.

In many everyday situations, Magyarul tanulok would be enough.

Tanulok is the 1st person singular present tense form of the verb tanul, meaning to learn or to study.

So:

• tanul = he/she learns, studies
• tanulok = I learn / I am learning / I study / I am studying

Hungarian does not normally make a sharp distinction here between learn and study the way English sometimes does. The exact meaning depends on context.

The ending -ok shows that the subject is I.

In other words, Hungarian often builds the subject information into the verb itself.

For example:

• tanulok = I learn
• tanulsz = you learn
• tanul = he/she learns
• tanulunk = we learn

That is why Én is optional: the verb already tells you who is doing the action.

Not exactly.

• magyar = Hungarian, Hungarian person, Hungarian language, depending on context
• magyarul = in Hungarian / Hungarianly in function, though in natural English we usually translate it as in Hungarian or sometimes just Hungarian

In sentences about languages, -ul / -ül often creates the form used to talk about doing something in a language:

• beszélek magyarul = I speak Hungarian
• olvasok magyarul = I read in Hungarian
• tanulok magyarul = I am learning Hungarian

So magyarul is the language-form used with many verbs.

The suffix -ul / -ül is commonly used with language names to mean in that language.

Examples:

• angol → angolul = in English
• német → németül = in German
• magyar → magyarul = in Hungarian

Which version appears, -ul or -ül, depends on vowel harmony and the shape of the word. You do not need to master all the details immediately; it is best to learn the language forms as vocabulary at first.

Because magyar by itself is not the normal form here.

When talking about using or learning a language, Hungarian often uses the language form with -ul / -ül:

• Beszélek magyarul.
• Írok magyarul.
• Tanulok magyarul.

So magyar tanulok would sound incomplete or ungrammatical in standard Hungarian.

Yes, and this is a very useful comparison.

• Magyarul tanulok = I am learning Hungarian
• Magyart tanulok = I study/learn Hungarian

Both can be used, but they are built differently:

• magyarul uses the language-form in Hungarian
• magyart is the direct object form of magyar

For a beginner, the important point is that Hungarian can express this idea in more than one way. In learning materials, magyarul tanulok is very common and natural.

Because Hungarian does not form the present continuous the way English does.

English often uses:

• I learn
• I am learning

Hungarian usually just uses the simple present form:

• tanulok

Depending on context, tanulok can mean:

• I learn
• I am learning
• I study
• I am studying

So there is no need for a separate word meaning am in this sentence.

Yes, you could. Hungarian word order is flexible, and different orders can change the emphasis.

For example:

• Én magyarul tanulok. = emphasis on I
• Magyarul tanulok. = neutral in many contexts, or emphasis on Hungarian
• Tanulok magyarul. = also possible, often a bit more conversational or context-dependent

Hungarian word order is not random, though. It often reflects what is being emphasized, contrasted, or presented as new information.

A simple approximate pronunciation is:

• Én ≈ ayn
• magyarul ≈ MAW-dyaw-rool
• tanulok ≈ TAW-noo-lok

A few helpful points:

• é is a long vowel, roughly like ay in say, but cleaner and without much glide
• gy is a special Hungarian consonant, somewhat like the d in British duke or a very soft dy
• a in Hungarian is closer to o in not than to English a in cat
• u is like oo in food
• stress in Hungarian usually falls on the first syllable: Én MAGyarul TAnulok

Because é is a different vowel from e in Hungarian.

The accent mark in Hungarian is not just decoration. It usually shows vowel quality and/or length, and it can change the word.

So:

• e and é are different vowels
• you should learn the accented letters as separate letters for practical purposes

In Én, the capital É is simply the uppercase form of é.

It can mean either, depending on context.

For example:

• Magyarul tanulok. = I am learning Hungarian / I study Hungarian
• Otthon tanulok. = I study at home

Hungarian often uses tanul for both the process of learning something and the activity of studying.

Because in Hungarian, names of languages and nationalities are usually not capitalized unless they begin the sentence.

So:

• magyar = Hungarian
• angol = English
• német = German

This is different from English, where Hungarian and English are capitalized.

So magyarul with a lowercase m is completely correct here.

Yes. It is a complete, grammatical sentence.

It contains:

• Én = subject pronoun
• magyarul = language-form
• tanulok = finite verb

In fact, Hungarian often allows even shorter complete sentences, because the verb ending carries so much information. For example:

• Tanulok. = I am learning / I study

So Én magyarul tanulok is fully complete and even slightly more explicit than necessary.