الكافيه جنب المحطة وهادي.

Yes. الكافيه means the café, and it is a borrowed word used very commonly in Egyptian Arabic.

• كافيه = café
• الـ = the
• so الكافيه = the café

A more formal/Standard Arabic word would be المقهى, but in everyday Egyptian, كافيه is very natural.

A natural pronunciation is:

el-kafēh gamb el-maḥaṭṭa wi hādi

A few useful notes:

• ج is usually pronounced g in Egyptian Arabic, so جنب sounds like gamb.
• المحطة is pronounced roughly el-maḥaṭṭa.
• و often sounds like wi or just w-.
• هادي sounds like hādi.

Because Arabic often leaves out is/am/are in the present tense.

So:

• الكافيه جنب المحطة وهادي literally looks like: the café next to the station and quiet
• but in natural English, that becomes: The café is next to the station and is quiet.

This is very normal in both Egyptian Arabic and Standard Arabic.

جنب means next to, beside, or by.

In this sentence:

• جنب المحطة = next to the station

In everyday Egyptian, جنب is a very common way to express location. You can think of it as a preposition-like word.

Because الـ is the Arabic definite article, meaning the.

So:

• الكافيه = the café
• المحطة = the station

Unlike English, Arabic attaches the directly to the beginning of the word.

هادي is the common Egyptian Arabic form of the adjective quiet/calm.

The Standard Arabic form is:

• هادئ

But in Egyptian Arabic, this is commonly said as:

• هادي

So this sentence sounds colloquial and natural in Egyptian speech.

Because هادي is a predicate adjective here, not an adjective directly attached inside the noun phrase.

In other words:

• الكافيه هادي = The café is quiet
• الكافيه الهادي = the quiet café

So in your sentence, هادي means is quiet, which is why it does not take الـ.

Yes. In Arabic, adjectives usually agree with the noun in gender and number.

Here, الكافيه is treated as masculine singular, so:

• هادي = masculine singular

If the noun were feminine, you would normally use:

• هادية = feminine singular

For example:

• القهوة هادية = The coffee shop is quiet

و means and.

So:

• وهادي = and quiet

In Arabic writing, و is attached directly to the following word. That is completely normal.

So you write:

• وهادي

not:

• و هادي

It is best understood as Egyptian Arabic or at least colloquial-style Arabic.

Clues:

• الكافيه is a common everyday borrowed word
• هادي is the Egyptian colloquial form of هادئ

A more Standard Arabic version would be something like:

المقهى بجانب المحطة وهادئ

Both mean the same thing, but your sentence sounds more natural for Egyptian everyday speech.

Yes, Arabic word order is somewhat flexible here.

Your sentence:

• الكافيه جنب المحطة وهادي

is natural and means:

• The café is next to the station and quiet.

You could also hear something like:

• الكافيه هادي وجنب المحطة

That would still be understandable. The difference is mainly in what is mentioned first, not in the basic meaning.