Én gyalog járok a könyvtárba.

Usually, no. Hungarian often leaves subject pronouns out because the verb already shows who the subject is.

So:

• Gyalog járok a könyvtárba. = a natural neutral sentence
• Én gyalog járok a könyvtárba. = I go to the library on foot

Including én adds emphasis or contrast. For example, it can suggest I go on foot, but someone else goes another way.

The verb ending tells you the person and number.

• járok = I go / I walk / I go regularly
• dictionary form: járni

Here the -ok ending marks first person singular: I.

That is why Hungarian can often omit én.

This is a very common question, because both can relate to going.

In this sentence, járok suggests a habitual or repeated action:

• járok a könyvtárba = I go to the library regularly / I am in the habit of going to the library
• megyek a könyvtárba = I am going to the library, often referring to a specific trip now or soon

So:

• Gyalog járok a könyvtárba. = I usually go to the library on foot
• Gyalog megyek a könyvtárba. = I’m going to the library on foot

Gyalog means on foot.

So gyalog járok is literally something like I go on foot.

In natural English, this is often translated as:

• I walk to the library
• I go to the library on foot

Hungarian uses gyalog where English often uses the phrase on foot.

Not quite.

• gyalog járok means your method of getting there is by walking
• sétálok means I stroll / I take a walk

So gyalog járok a könyvtárba focuses on transportation: walking instead of driving, taking the bus, etc.

If you say a könyvtárba sétálok, it can sound more like I’m strolling to the library, which has a different feel.

Because the sentence expresses movement toward and into a place.

Hungarian uses:

• -ba / -be = into, to
• -ban / -ben = in, inside

So:

• a könyvtárba = to / into the library
• a könyvtárban = in the library

Compare:

• A könyvtárba járok. = I go to the library.
• A könyvtárban vagyok. = I am in the library.

A is the Hungarian definite article, like English the.

• a könyvtárba = to the library

Hungarian has two forms of the definite article:

• a before consonants
• az before vowels

Since könyvtár begins with k, it takes a, not az.

Sometimes yes, but the nuance changes.

• a könyvtárba usually points to a specific or contextually known library: the library
• könyvtárba without the article can sound more general, depending on context: to a library or just library in a more general sense

In your sentence, a könyvtárba is the most straightforward way to say to the library.

Most naturally, it describes a habit or usual pattern.

Because of járok, the sentence usually means something like:

• I usually go to the library on foot
• I walk to the library

If you want to describe what you are doing right now, Hungarian would more naturally use megyek:

• Gyalog megyek a könyvtárba. = I’m going to the library on foot.

Yes. Hungarian word order is flexible, and changes in word order often change emphasis, not the basic meaning.

For example:

• Gyalog járok a könyvtárba. = neutral; the walking part is prominent
• Én gyalog járok a könyvtárba. = emphasis on I
• A könyvtárba gyalog járok. = emphasis on to the library
• Én a könyvtárba gyalog járok. = possible in a contrastive context

So the original sentence is grammatical, but it is not the only possible order.

A more neutral version would often be:

• Gyalog járok a könyvtárba.

That is because én is usually omitted unless you want emphasis or contrast.

So:

• Én gyalog járok a könyvtárba. = I go to the library on foot.
• Gyalog járok a könyvtárba. = I go to the library on foot.

Both are correct; the second is just less emphatic.

A few sounds may stand out to English speakers:

• Én: é is a long vowel, roughly like ay in say, but pure and not gliding
• gy in gyalog: a soft sound somewhat like dy in duke in some accents, though not exactly the same
• ny in könyvtárba: like ny in canyon
• á in jár and -tár-: a long open a, somewhat like a in father
• ö in könyv-: a rounded front vowel, with no exact English equivalent

A rough learner-friendly approximation might be:

• Én ≈ ayn
• gyalog ≈ dyaw-log
• könyvtárba ≈ kuhnyv-taar-baw

That is only approximate, but it helps you get started.