الحديقة خضرا.

A natural Egyptian pronunciation is el-ḥadīʔa khaḍra.

A few helpful sound notes:

• الـ is usually pronounced el- or il-, not al-.
• ح is a stronger, breathier h sound.
• ق in Egyptian Arabic is often a glottal stop ʔ, so حديقة sounds like ḥadīʔa.
• خ is the throaty kh sound, like in Scottish loch or German Bach.

So the whole sentence sounds roughly like: el-ha-DEE-a KHAD-ra.

Because Arabic usually leaves out the present-tense verb to be.

So:

• الحديقة خضرا = The garden is green

There is no separate word for is in simple present-tense sentences like this.

But in other tenses, Arabic does use a verb:

• الحديقة كانت خضرا = The garden was green
• الحديقة هتكون خضرا = The garden will be green

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

Because الحديقة is feminine, and the adjective has to match it.

• Masculine: أخضر = green
• Feminine: خضرا = green

Since الحديقة is a feminine noun, you use the feminine adjective:

• الحديقة خضرا

One clue that الحديقة is feminine is the ending ـة. Nouns ending in ـة are very often feminine.

Because خضرا here is not being used as part of a noun phrase like the green garden. It is the predicate: green in The garden is green.

So:

• الحديقة خضرا = The garden is green
• الحديقة الخضرا = the green garden

That is an important difference in Arabic:

• noun + adjective without الـ can make a full sentence
• noun + adjective with matching الـ makes a noun phrase

So الحديقة خضرا is a complete sentence, while الحديقة الخضرا is just a phrase.

خضرا is the Egyptian Arabic form.
خضراء is the Standard Arabic form.

So:

• Egyptian Arabic: الحديقة خضرا
• Standard Arabic: الحديقة خضراء

This is a very common difference between colloquial Egyptian and Standard Arabic. In everyday Egyptian speech, خضرا is what you would normally expect.

الحديقة is understood in Egyptian Arabic, but it sounds a bit more formal or bookish than some everyday choices.

In very natural everyday Egyptian, many speakers would often say:

• الجنينة خضرا = The garden is green

So:

• الحديقة خضرا = correct and understandable
• الجنينة خضرا = often more conversational in daily Egyptian speech

The difference is sentence vs phrase.

• الحديقة خضرا = The garden is green
  This is a full sentence.

• الحديقة الخضرا = the green garden
  This is just a noun phrase.

A good way to remember it:

• If the second word is the description after is, it usually does not take الـ
• If the second word is directly describing the noun inside the same phrase, it does take الـ

Yes. This is a very common pattern in Egyptian Arabic:

definite noun + adjective = The noun is adjective

For example:

• العربية سريعة = The car is fast
• الأوضة نضيفة = The room is clean
• الشجرة طويلة = The tree is tall

So الحديقة خضرا follows a very useful basic pattern.