أهمية النادي واضحة.

Because this is a nominal sentence in Arabic. In the present tense, Arabic often says X Y instead of X is Y.

So:

• أهمية النادي = the importance of the club
• واضحة = clear / obvious

Together, it means The importance of the club is clear or The club’s importance is clear.

Arabic usually leaves out the present-tense is/are.

This is an iḍāfa construction, often called a genitive construction or possessive phrase.

It is made of:

• أهمية = importance
• النادي = the club

Together: the importance of the club / the club’s importance

In an iḍāfa:

1. the first noun is the thing being possessed or defined
2. the second noun tells whose/what it is
3. the second noun is in the genitive case

So أهمية النادي literally works like importance of the club.

In an iḍāfa, the first noun usually does not take ال. The definiteness of the whole phrase is determined by the second noun.

Here:

• النادي has الـ
• so the whole phrase أهمية النادي becomes definite: the importance of the club

This is a very important pattern in Arabic:

• أهمية نادٍ = importance of a club / a club’s importance
• أهمية النادي = the importance of the club

So the phrase is definite even though أهمية itself does not have الـ.

Because it describes أهمية, and أهمية is a feminine noun.

In Arabic, adjectives must agree with the noun they describe in:

• gender
• number
• definiteness
• case

Since أهمية is feminine singular, the adjective is also feminine singular:

• masculine: واضح
• feminine: واضحة

So أهمية ... واضحة is correct agreement.

Grammatically, it is the predicate of the sentence, but it is a word of the type we usually call an adjective.

In this sentence:

• أهمية النادي = the subject/topic
• واضحة = the predicate/comment

So it is not modifying a noun inside the phrase in the same way as a clear importance would. Instead, it is saying something about the subject:

• The importance of the club is clear

That is why many learners think of it as an adjective used predicatively.

A fully vocalized version would usually be:

أهميّةُ النّادي واضحةٌ

Case breakdown:

• أهميّةُ: nominative, because it is the subject of the nominal sentence
• النّادي: genitive, because it is the second term of the iḍāfa
• واضحةٌ: nominative, because it is the predicate of the nominal sentence

So the endings are:

• ـُ on أهمية
• ـِ implied on النادي in structure, though the written ending of this noun appears as ـي
• ـٌ on واضحة

In normal unvocalized writing, these short vowels are usually not written.

Because the word is النادي and its final letter is ي.

It is pronounced approximately an-naadii.

A few helpful points:

• الـ = al-, but here it assimilates to the n sound because ن is a sun letter
• so النادي is pronounced an-naadii, not al-naadii
• the ending ـي gives the long ii sound

So the whole word sounds like an-naa-dii.

Because ن is one of the sun letters. When الـ comes before a sun letter, the l sound is not pronounced, and the following consonant is doubled.

So:

• written: النادي
• pronounced: an-naadii

This is a pronunciation rule, not a spelling change. The spelling still keeps الـ.

Not directly. The sentence specifically says:

• أهمية النادي = the importance of the club
• واضحة = is clear / obvious

So the meaning is specifically about the importance being clear.

If you wanted to say The club is important, you would say something like:

• النادي مهمّ

If you wanted The club’s importance is obvious, then أهمية النادي واضحة is exactly that.

Yes. In this sentence, واضحة can naturally mean:

• clear
• obvious
• evident

The best English choice depends on context.

So these are all reasonable translations:

• The importance of the club is clear.
• The club’s importance is obvious.
• The importance of the club is evident.

Yes, Arabic can sometimes change word order for emphasis.

The neutral order here is:

• أهمية النادي واضحة

You could also say:

• واضحةٌ أهميةُ النادي

This is less neutral and more rhetorical or literary. It puts extra focus on واضحة.

For most learners, the original order is the most natural one to use first.

Because أهمية is the first term of an iḍāfa, and the first term of an iḍāfa does not take tanwīn.

Compare:

• أهميةٌ = an importance
• أهميةُ النادي = the importance of the club

Once أهمية becomes the first part of the possessive construction, tanwīn disappears.

This is a key sign that a noun may be in iḍāfa.

النادي usually means the club.

Depending on context, it could refer to:

• a sports club
• a social club
• an organization or association
• sometimes a cultural club or student club

So the sentence itself does not tell you what kind of club it is. Context does that.

A simple breakdown is:

• أهمية النادي = subject of the sentence
• واضحة = predicate

More traditional Arabic grammar terms would be:

• أهمية النادي = مبتدأ phrase
• واضحة = خبر

Inside the first phrase:

• أهمية = first term of the iḍāfa
• النادي = second term of the iḍāfa

So the sentence is basically:

• [The importance of the club] [is clear].

Yes, واضح would be wrong in this sentence if it refers to أهمية.

That is because:

• أهمية is feminine
• the adjective/predicate must agree with it
• so you need واضحة

Compare:

• الأمر واضح = The matter is clear
  
  • الأمر is masculine, so واضح
• الأهمية واضحة = The importance is clear
  
  • الأهمية is feminine, so واضحة

So agreement is the reason.