سوء الطقس مشكلة.

Because this is a present-tense nominal sentence in Arabic. In sentences like this, Arabic usually leaves out the verb to be.

So:

• سوء الطقس مشكلة = Bad weather is a problem

If you wanted a past tense, you would normally use كان:

• كان سوء الطقس مشكلة = Bad weather was a problem

It is a nominal sentence made of two parts:

• سوء الطقس = the subject/topic (مبتدأ)
• مشكلة = the predicate/comment (خبر)

So the structure is:

• [subject] + [predicate]
• سوء الطقس + مشكلة

A fully vocalized version would be:

• سُوءُ الطَّقْسِ مُشْكِلَةٌ

Yes. سوء الطقس is one noun phrase.

It is an iḍāfa (construct phrase), where:

• سوء = badness, سوء, poor condition
• الطقس = the weather

Literally, it is something like:

• the badness of the weather

But in natural English, that is usually just:

• bad weather

So this is not an adjective + noun phrase like bad weather in English. It is a noun + noun structure in Arabic.

No. سوء is a noun, not an adjective.

It means something like:

• badness
• poor quality
• evil or harm in some contexts

Here it gives the idea of bad weather through the iḍāfa phrase سوء الطقس.

If you wanted a more straightforward adjective-based phrase, you could say:

• الطقس السيئ = the bad weather

So:

• سوء الطقس = a noun-based expression
• الطقس السيئ = an adjective-based expression

Because Arabic does not need a separate word for of in an iḍāfa construction.

In English, you might say:

• the badness of the weather

In Arabic, the relationship is shown just by putting the two nouns together:

• سوء الطقس

So Arabic expresses of here through grammar, not through a separate word.

Because in an iḍāfa, the second noun is automatically genitive.

So in:

• سُوءُ الطَّقْسِ

the word الطقسِ takes the genitive ending because it is the second term of the construct phrase.

That is why, in fully vocalized Arabic, you get:

• سُوءُ = nominative
• الطَّقْسِ = genitive

Because سوء is the first term of an iḍāfa.

In an iḍāfa, the first noun:

• normally does not take الـ
• does not take tanwīn

So you get:

• سوء الطقس not
• السوء الطقس and not
• سوءٌ الطقس

Also, the definiteness of the whole phrase depends on the second noun. Since الطقس has الـ, the whole phrase سوء الطقس is definite.

Because the sentence is saying that bad weather is a problem, not the problem.

So:

• مشكلة = a problem
• المشكلة = the problem

Using an indefinite predicate is very common when you are classifying or describing something:

• زيد طالب = Zayd is a student
• سوء الطقس مشكلة = Bad weather is a problem

If you said:

• سوء الطقس هو المشكلة or
• سوء الطقس المشكلة

that would mean something closer to:

• Bad weather is the problem

which is more specific.

It is a noun here.

• مشكلة = a problem

So the sentence means:

• Bad weather is a problem

It is not describing سوء الطقس with an adjective. It is identifying it as a thing: a problem.

Also, مشكلة is a feminine noun by itself. Its feminine form is part of the word; it is not feminine because it is agreeing with سوء الطقس.

A careful pronunciation with case endings is:

• sūʾu ṭ-ṭaqsi mushkilatun

A few useful notes:

• سوء has a long ū sound, then a hamza: sūʾ
• الطقس is pronounced aṭ-ṭaqs, because ط is a sun letter, so the l of ال is not pronounced
• In normal pause, speakers often drop final case endings, so you may hear something closer to:
  • sūʾ aṭ-ṭaqs mushkila(h)

Yes, absolutely.

• الطقس السيئ مشكلة = The bad weather is a problem
• سوء الطقس مشكلة = Bad weather is a problem

Both are natural, but they are built differently:

• الطقس السيئ uses an adjective (السيئ = bad)
• سوء الطقس uses a noun (سوء = badness/poor condition)

The version with سوء can sound a bit more formal or abstract.

The full form is:

• سُوءُ الطَّقْسِ مُشْكِلَةٌ

The endings are:

• سوءُ = nominative, because it is the مبتدأ and also the first term of the iḍāfa
• الطقسِ = genitive, because it is the second term of the iḍāfa
• مشكلةٌ = nominative, because it is the خبر

So the pattern is:

• nominative + genitive + nominative