هاد الجزء صغير.

Yes. هاد is a Levantine form of this for a masculine singular noun. It corresponds to MSA هذا.

In different parts of the Levant, you may also hear forms like هيدا or the attached form هالـ. In this sentence, هاد points to الجزء, which is masculine singular.

That is normal Arabic structure.

When a demonstrative like هاد comes before a noun, the noun is usually definite, so it takes الـ:

• هاد الجزء = this part
• literally: this the-part

So even though it sounds unusual from an English point of view, it is the expected pattern.

In Arabic, the verb to be is usually not said in the present tense.

So:

• هاد الجزء صغير
• literally: this part small
• natural English: This part is small

This kind of sentence is called a nominal sentence or verbless sentence in the present tense.

Because صغير is describing the subject هاد الجزء as the predicate of the sentence.

Arabic commonly puts things in this pattern:

subject + description

So:

• هاد الجزء = the subject
• صغير = what is being said about it

That gives:

• هاد الجزء صغير = This part is small

This is a very important difference:

• الجزء الصغير = the small part
  • here الصغير is a regular adjective directly modifying الجزء
• الجزء صغير = the part is small
  • here صغير is the predicate of a full sentence

So in your sentence, صغير does not take الـ because it is not part of a noun phrase like the small part. It is the statement being made about the part.

Yes, they have to agree with the noun.

Since الجزء is masculine singular, the sentence uses:

• هاد for this masculine singular
• صغير for small masculine singular

If the noun were feminine, you would change both:

• هاي القطعة صغيرة = This piece/part is small

So agreement is something you should always watch in Arabic.

A rough pronunciation is:

• هاد → haad
• الجزء → il-juzʔ or el-juzʔ
• صغير → often something like sghīr or zghīr in Levantine pronunciation, depending on region and speaker

So the whole sentence is roughly:

haad il-juzʔ sghīr

The last sound in جزء is a hamza ء, a small glottal stop. In fast speech, some speakers make it lighter.

Yes, absolutely. هالـ is a very common colloquial Levantine way to say this + noun.

So:

• هاد الجزء صغير
• هالجزء صغير

Both are understandable. In many contexts, هالجزء صغير sounds even more everyday and natural.

It is definitely understandable and fine, but it feels a bit mixed:

• هاد is clearly colloquial Levantine
• الجزء is also used, but it is a word shared with MSA and can feel a bit more neutral or slightly formal

So the sentence works well, but in very casual speech many speakers might prefer:

• هالجزء صغير

Still, the version you have is perfectly useful for learning.

Yes, in Levantine you can also hear the demonstrative after the noun:

• الجزء هاد صغير

This also means this part is small.

That word order is common in spoken Levantine, often with a slightly more specific or pointing feel. For a learner, though, هاد الجزء صغير is a very clear pattern to start with.