بدي هاد الجزء.

بدي is the very common Levantine way to say I want, and depending on context it can also feel like I need or I'd like.

Grammatically, it works like a fixed colloquial pattern with attached pronouns:

• بدي = I want
• بدك = you want
• بده = he wants
• بدها = she wants
• بدنا = we want

So in this sentence, بدي already includes the subject I.

It is usually pronounced something like baddi or, in some areas, closer to biddi.

A few helpful points:

• The د is effectively doubled in pronunciation.
• Everyday Arabic spelling often leaves out short vowels and doubling marks, so بدي is written simply like that even though the spoken form is heavier than a simple badi.
• A good learner pronunciation is BAD-di.

هاد is a Levantine colloquial form of this.
هذا is the Standard Arabic form.

So:

• هاد = colloquial Levantine
• هذا = Standard Arabic

You will also hear هادا in many Levantine varieties. So هاد and هادا are both normal depending on region and speaking style.

Because الجزء is a masculine singular noun, and هاد is the common masculine singular demonstrative this in Levantine.

If the noun were feminine, you would usually hear something like:

• هاي
• هادي

For example:

• هاي القطعة = this piece

And for plural, you often hear:

• هدول = these

Because in Arabic, after a demonstrative like this, the noun is normally still definite.

So Arabic says something structurally like:

• this the-part

That is normal Arabic grammar, even though English does not do it that way.

So هاد الجزء is exactly what you should expect, not a mistake.

Yes — and in fact هالجزء is very common in Levantine.

هالـ is basically a fused colloquial form used before nouns, meaning this + the.

So these are both natural:

• هاد الجزء
• هالجزء

In fast, everyday speech, many speakers prefer هالجزء.

It is understandable and natural, but it can feel a bit more neutral/formal/shared-Arabic than some very everyday dialect words.

That is common in Levantine: speakers often use colloquial grammar with vocabulary that is also used in Standard Arabic.

So this sentence is still perfectly normal Levantine because of words like:

• بدي
• هاد

But الجزء itself is not strongly dialect-only. Depending on context, a speaker might also choose a more conversational word such as:

• قطعة for a physical piece
• قسم for a section
• فقرة for a paragraph/segment

It depends on what kind of part is meant.

Yes, you may hear that in some varieties or for emphasis, but for a learner the safest default is:

• هاد الجزء
• or هالجزء

When the demonstrative comes after the noun, as in الجزء هاد, it can sound more like this part here / this particular part.

So:

• بدي هاد الجزء = very straightforward
• بدي هالجزء = very common everyday form
• بدي الجزء هاد = possible, often more colloquial or emphatic

No. You do not need أنا here, because بدي already tells you the subject is I.

So:

• بدي هاد الجزء = completely normal
• أنا بدي هاد الجزء = also correct, but now أنا adds emphasis or contrast

For example, you might say أنا if you want to stress that I want this part, not someone else.

A careful pronunciation is something like il-juzʔ or el-juzʔ, depending on the region.

Useful details:

• ج in Levantine is usually like English j
• the ل in الـ is pronounced here, because ج is a moon letter, not a sun letter
• the final ء is a glottal stop, though in fast speech some speakers may weaken it

So a good learner pronunciation is roughly:

• il-juz'
• or el-juz'

The Standard Arabic equivalent would be:

• أريد هذا الجزء

That helps show what is specifically Levantine here:

• بدي instead of أريد
• هاد instead of هذا

So the sentence you were given is clearly colloquial Levantine, not formal Standard Arabic.