حضرتك بدك كاسة مي من التلاجة؟

It is colloquial Levantine Arabic, not Modern Standard Arabic.

A few clues:

• بدك is a Levantine colloquial way to say you want
• مي is the everyday Levantine word for water
• التلاجة is a colloquial word for the fridge
• The whole sentence sounds natural in spoken conversation, especially in daily life

In Modern Standard Arabic, the wording would be quite different.

حضرتك is a polite way to say you. Literally, it comes from the idea of your presence, but in everyday Levantine it functions as a respectful form of address.

It is commonly used:

• with customers
• with older people
• with someone you want to speak to politely

So it adds politeness, similar to the difference between Do you want... ? and Would you like... ? in English.

Yes, that mix is completely normal.

In Levantine speech, حضرتك is a polite word, but people still usually use ordinary colloquial grammar with it. So حضرتك بدك...؟ sounds natural and common.

It does not mean the speaker is switching into formal Arabic. It just means they are being polite in everyday speech.

بدك means you want.

It comes from the Levantine word بدّ plus a pronoun ending:

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

So in this sentence, بدك is the main part that expresses wanting.

Yes, in pronunciation it does.

In normal Levantine speech:

• to a man: بدك is pronounced baddak
• to a woman: بدك is pronounced baddik

But in everyday Arabic writing, both are often written the same way: بدك.

So the written form may look identical, while the spoken form tells you the gender.

Arabic does not have an indefinite article like English a/an.

So كاسة by itself can mean:

• a cup
• a glass

The noun is indefinite simply because it does not have ال at the beginning.

So:

• كاسة = a cup / a glass
• الكاسة = the cup / the glass

Arabic often expresses this idea by putting two nouns together, without a separate word for of.

So كاسة مي is literally something like:

• cup water but it naturally means
• a cup/glass of water

This is very normal in Arabic. English needs of, but Arabic often does not.

It can mean either, depending on context.

In many Levantine contexts, كاسة is a general everyday word for a drinking container. With water, English might translate it as either:

• a glass of water
• a cup of water

If the exact container matters, speakers can choose a more specific word, but here كاسة is perfectly natural and everyday.

Because مي is the normal everyday Levantine word for water.

• مي is what people say in conversation
• ماء is the formal or Standard Arabic word

So if you are learning spoken Levantine, مي is the form you will hear all the time.

من التلاجة means from the fridge.

It tells you what kind of water is being offered: water that comes from the fridge, so probably cold water.

Without it, بدك كاسة مي؟ would simply mean Do you want a glass of water? With من التلاجة, it becomes more specific: Do you want a glass of water from the fridge?

Because the speaker means a specific, known fridge: the fridge.

In a home or workplace, there is usually one obvious fridge, so using ال is natural.

So:

• تلاجة = a fridge
• التلاجة = the fridge

Also, because ت is a sun letter, the ل in ال is not clearly pronounced in speech. So التلاجة is pronounced more like et-tallāje or it-tallāje, depending on accent.

In Arabic, yes/no questions often look just like statements, and they are understood as questions through:

• intonation in speech
• context
• a question mark in writing

So حضرتك بدك كاسة مي من التلاجة؟ is a yes/no question simply because it is said with questioning intonation.

This is very common in Levantine Arabic.

No extra verb is required here.

Arabic can say بدك كاسة مي؟ literally with just the idea you want a glass of water? and that is fully natural.

English sometimes prefers to say:

• Do you want a glass of water?
• Would you like a glass of water?

But Levantine does not need a separate verb such as drink in this sentence.

It is polite but still everyday and conversational.

The politeness mainly comes from حضرتك. The rest of the sentence is ordinary spoken Levantine, so it does not sound stiff or overly formal.

This kind of sentence would be very natural if you were:

• offering water to a guest
• speaking politely to a customer
• talking respectfully to someone older or less familiar

So the overall tone is warm, normal, and polite.