الناس في السوق اليوم.

Yes. In Modern Standard Arabic, a present-tense sentence like this often has no verb for to be.

So:

الناس في السوق اليوم
literally: the people in the market today

naturally means:

The people are in the market today.

This is called a nominal sentence. Here:

• الناس = the subject/topic
• في السوق = the predicate/comment
• اليوم = a time expression, today

If you wanted the past or future, Arabic would usually add a verb such as كان or سيكون.

الناس means people.

It is a very common word and usually refers to people as a group, not one person. It is not the normal way to say a person. For a person, Arabic would usually use words like:

• شخص = person
• إنسان = human being

With ال-, الناس often means the people or people in general, depending on context.

Because ال- is the Arabic definite article, meaning the.

So:

• الناس = the people
• السوق = the market

A native English speaker may expect fewer definite articles, but Arabic often uses ال- in places where English may or may not use the, depending on style and context.

Also, being after a preposition like في does not remove ال-. So في السوق simply means in the market or at the market.

في basically means in.

But in English, with places, the best translation may be in or at, depending on what sounds natural.

So:

• في السوق can be understood as in the market
• and in many contexts also at the market

Arabic uses في very commonly for location.

Yes, it could go somewhere else. Arabic word order is fairly flexible.

Putting اليوم at the end is very natural and neutral:

الناس في السوق اليوم
= The people are in the market today.

You could also move it earlier for emphasis:

اليوم الناس في السوق
= Today, the people are in the market.

The basic meaning stays the same, but the emphasis changes.

The pronunciation changes because of sun letters.

In this sentence:

• الناس is pronounced roughly an-naas
• السوق is pronounced roughly as-suuq
• اليوم is pronounced al-yawm

That happens because:

• ن in الناس is a sun letter, so the l of ال- is assimilated
• س in السوق is also a sun letter, so the l is assimilated there too
• ي in اليوم is not a sun letter, so the l is pronounced normally

So a normal pronunciation of the whole sentence is roughly:

an-naasu fii s-suuqi al-yawma

In pause, learners often hear something closer to:

an-naas fii s-suuq al-yawm

Fully vocalized, the sentence is:

النّاسُ في السّوقِ اليومَ

The endings are:

• النّاسُ: nominative, because it is the subject/topic
• السّوقِ: genitive, because it comes after في
• اليومَ: accusative, because it functions as an adverb of time

In normal everyday writing, these short vowels are usually not written, so you will often just see:

الناس في السوق اليوم

As a learner, it is useful to understand the endings, even if you do not always pronounce them in less formal situations.

Yes. In this sentence, في السوق is a prepositional phrase functioning as the predicate.

So the structure is:

• الناس = subject/topic
• في السوق = predicate
• اليوم = time expression

This is very common in Arabic. A prepositional phrase can act as the main comment about the subject, even without a verb in the present tense.