مدة المعالجة مهمة لمقدم الطلب.

Because this is a nominal sentence in Arabic. In the present tense, Arabic usually does not use a separate word for is/are.

So:

• مدة المعالجة = the processing time
• مهمة = important

Together, مدة المعالجة مهمة means The processing time is important.

If you wanted a past or future meaning, then Arabic would use a verb such as كان.

Because مدة المعالجة is an iḍāfa construction, often called a construct phrase.

In an iḍāfa:

• the first noun normally does not take الـ
• the second noun determines whether the whole phrase is definite or indefinite

So here:

• مدة = duration / period
• المعالجة = the processing

Together:

• مدة المعالجة = the duration of the processing, or more naturally, the processing time

Even though مدة has no الـ, the whole phrase is definite because المعالجة is definite.

It is an iḍāfa phrase made of two nouns:

• مدة = duration, period, length
• المعالجة = the processing, the treatment, the handling

Literally, it means duration of the processing.

In this structure:

• the first noun is the main thing being talked about
• the second noun specifies it

So مدة المعالجة is a very natural Arabic way to say processing time.

Because مدة is a feminine noun, and the predicate adjective agrees with it in gender.

So:

• مهم = important masculine
• مهمة = important feminine

Since the subject is مدة, the correct form is مهمة.

This agreement is very common in Arabic, even when the noun is not referring to a female person.

Because it is the predicate of the sentence, not part of the noun phrase مدة المعالجة.

In simple Arabic sentences of the type X is Y, the predicate is often indefinite:

• الكتاب جديد = The book is new
• المدينة كبيرة = The city is big
• مدة المعالجة مهمة = The processing time is important

So even though مدة المعالجة is definite, مهمة does not need الـ.

Here لـ means for or to, depending on how you translate it in English.

So:

• لمقدم الطلب = for the applicant

It shows who this is important for. In Arabic, لـ is very often used this way to indicate the person affected or concerned.

Also, after لـ, the following noun is in the genitive case.

Literally, it means the submitter of the application/request.

It is another iḍāfa:

• مقدم = submitter / presenter
• الطلب = the request / the application

So مقدم الطلب is a formal way to say applicant.

In fully vowelled Arabic, this is usually read as مُقَدِّم الطلب (muqaddim aṭ-ṭalab), meaning the one who submits the application.

It can mean both, depending on context.

Common possibilities include:

• request
• application
• petition
• demand in some contexts

In administrative or immigration-style language, مقدم الطلب is very often best translated as applicant, so الطلب there is often understood as application.

With full vowel marks, it would be:

مُدَّةُ المُعَالَجَةِ مُهِمَّةٌ لِمُقَدِّمِ الطَّلَبِ

A careful pronunciation is roughly:

muddatu l-muʿālajati muhimmatun li-muqaddimi ṭ-ṭalabi

A few useful things to notice:

• مدةُ is nominative because it is the subject
• المعالجةِ is genitive because it is the second part of an iḍāfa
• مهمةٌ is nominative because it is the predicate
• مقدمِ is genitive after لِ
• الطلبِ is also genitive because it is the second part of another iḍāfa

In normal unvowelled writing, these endings are usually not shown.

Yes, but the given order is the most straightforward and neutral.

The sentence is structured as:

• مدة المعالجة = subject
• مهمة = predicate
• لمقدم الطلب = prepositional phrase adding for the applicant

So the basic meaning is:

The processing time is important for the applicant.

Arabic can move parts around for emphasis, but this version is a very natural standard one.