Hij draagt bruine schoenen.

Because the verb has to match hij (he).

The infinitive is dragen = to wear / to carry.

In the present tense:

• ik draag = I wear
• jij draagt = you wear
• hij draagt = he wears
• wij dragen = we wear

So with hij, you use draagt.

Here, dragen means to wear.

But dragen is a broader verb than English wear. It can also mean:

• to carry
• to bear
• to support

Examples:

• Hij draagt een jas. = He is wearing a coat.
• Hij draagt een tas. = He is carrying a bag.

So the exact meaning depends on what follows the verb. With schoenen (shoes), wear is the natural meaning.

Because the adjective comes before a plural noun.

• bruin = brown
• bruine schoenen = brown shoes

In Dutch, adjectives before plural nouns normally take -e:

• een groot huis = a big house
• grote huizen = big houses
• bruine schoenen = brown shoes

So schoenen is plural, and that is why you get bruine.

Because the sentence is talking about brown shoes in a general, indefinite way, not a specific known pair.

• Hij draagt bruine schoenen. = He is wearing brown shoes.
• Hij draagt de bruine schoenen. = He is wearing the brown shoes.

Dutch often leaves out the article in plural indefinite nouns, just like English:

• I see dogs.
• Ik zie honden.

So bruine schoenen here means brown shoes / some brown shoes, not the brown shoes.

It can mean either one, depending on context.

Dutch present tense often covers both:

• a general habit: He wears brown shoes
• something happening now: He is wearing brown shoes

If you want to make right now clearer, Dutch can also use:

• Hij heeft bruine schoenen aan.

That is also very common for clothing.

Both are correct, but they can feel slightly different.

• Hij draagt bruine schoenen.
  A bit more neutral or descriptive. It can sound like a statement about what he is wearing, or even about his usual style.

• Hij heeft bruine schoenen aan.
  Very common in everyday speech for what someone has on at the moment.

So if you are just describing someone’s outfit right now, Hij heeft bruine schoenen aan is often especially natural. But Hij draagt bruine schoenen is absolutely good Dutch.

It follows normal Dutch main-clause word order:

• Hij = subject
• draagt = finite verb
• bruine schoenen = object

So the pattern is:

Subject + verb + object

That is the same basic order as in English:

• He wears brown shoes.

Dutch main clauses usually put the conjugated verb in the second position, and this sentence follows that rule perfectly.

Because schoen (shoe) makes its plural as schoenen (shoes).

This is a very common Dutch plural pattern:

• singular schoen
• plural schoenen

Other examples:

• tafel → tafels
• kat → katten
• schoen → schoenen

So schoenen is simply the regular plural form here.

Roughly like draakht, with a harsh Dutch g/ch sound near the end.

A few parts:

• dr = similar to English dr
• aa = a long ah sound
• gt = in normal speech, this often sounds like a rough cht sound plus t

So English speakers often approximate it as:

• draa-kht

The exact sound depends a bit on accent, but the key thing is that it does not sound like English dragt with a normal hard g.

No, not if you mean brown shoes in the normal sense.

Since people normally wear two shoes, Dutch uses the plural:

• Hij draagt bruine schoenen.

If you used singular, it would mean one brown shoe:

• Hij draagt een bruine schoen.

That is grammatically possible, but it means he is wearing only one brown shoe, which is unusual unless that is exactly what you want to say.

Because hij is the Dutch subject pronoun meaning he.

Dutch subject pronouns include:

• ik = I
• jij/je = you
• hij = he
• zij/ze = she / they
• wij/we = we

Since hij is the subject of the sentence, it appears at the start:

• Hij draagt bruine schoenen. = He wears/is wearing brown shoes.

If it were him instead of he, Dutch would use a different form, such as hem, but not as the subject of this sentence.