تخانة الحافة مهمة.

تخانة is a very common Egyptian Arabic word for thickness.
A learner may also know سُمك, which is another word for thickness, and is often felt to be more MSA/formal or more neutral across varieties.

So in Egyptian:

• تخانة = thickness, how thick something is
• سُمك = thickness too, but often sounds a bit more formal or technical depending on context

In everyday Egyptian speech, تخانة is very natural.

الحافة means the edge, the rim, or the border of something, depending on context.

For example, it could refer to:

• the edge of a table
• the rim of a cup
• the edge of a piece of material

So in this sentence, الحافة is the edge/rim whose thickness is being talked about.

الـ is the Arabic definite article, meaning the.

So:

• حافة = an edge / a rim
• الحافة = the edge / the rim

Because the sentence says the edge, Arabic uses الـ.

Because the thing being described is feminine.

The subject here is effectively تخانة الحافة = the thickness of the edge.
The main noun in that phrase is تخانة, and تخانة is feminine.

So the adjective/predicate must agree with it:

• مهمة = important (feminine)
• مهم = important (masculine)

That is why the sentence says مهمة, not مهم.

Yes. This is an idafa-type structure, which is very common in Arabic.

• تخانة = thickness
• الحافة = the edge

Together:

• تخانة الحافة = the thickness of the edge / the edge's thickness

Arabic often expresses possession or of relationships by simply putting two nouns together.

Because Arabic often uses nominal sentences in the present tense with no written or spoken verb for "is".

So:

• تخانة الحافة مهمة literally looks like the thickness of the edge important
• but it means The thickness of the edge is important

This is completely normal in Arabic.
In the present tense, is/are is usually omitted.

Yes. This is a very normal Arabic sentence pattern.

It goes like this:

• تخانة الحافة = subject/topic
• مهمة = predicate/comment

So the structure is:

• [noun phrase] + [adjective/predicate]

That is a standard way to say X is important, X is big, X is expensive, etc.

A common pronunciation is approximately:

• takhāna or tekhāna, depending on how you hear/transcribe Egyptian vowels

A rough breakdown:

• ت = t
• خ = a throaty kh sound, like German Bach or Scottish loch
• انة gives the long aa plus final -a

So the whole word is roughly ta-KHAA-na.

A common pronunciation is roughly:

• el-ḥāffa

In Egyptian Arabic, الـ is often pronounced el-.

Here the ل does not assimilate, because ح is a moon letter, not a sun letter.

So you pronounce the l clearly:

• الحافة → el-ḥāffa

Also, the ح is a strong breathy h sound from deeper in the throat than English h.

Because the word contains a shadda on ف: الحافّة.

That means the f sound is doubled or held slightly longer:

• ḥāfa would be different
• ḥāffa is the actual pronunciation here

This doubling is part of the word itself, so it should be pronounced.

Yes, it can sound natural, especially in technical, practical, or descriptive contexts.

For example, someone might say it when talking about:

• a phone case
• a piece of furniture
• a tool
• packaging
• a medical or design detail

Depending on context, Egyptians might also say similar things like:

• تخانة الحافة مهمة جدًا = The edge thickness is very important.
• مهم تخانة الحافة تبقى مناسبة = It’s important that the edge thickness be suitable.

But the given sentence itself is perfectly understandable and natural.