تشوش الرؤية وطول النظر مشكلتان.

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

So:

• تشوش الرؤية وطول النظر مشكلتان = Blurred vision and farsightedness are two problems

If you wanted were or will be, then Arabic would use words like كان or سيكون.

The sentence has two main parts:

• تشوش الرؤية وطول النظر = the subject
• مشكلتان = the predicate

More specifically, the subject is a compound subject made of two things joined by و (and):

• تشوش الرؤية
• طول النظر

Then مشكلتان tells you what those two things are: two problems.

Because the sentence is talking about exactly two things:

1. تشوش الرؤية
2. طول النظر

So Arabic uses the dual form of مشكلة:

• singular: مشكلة = a problem
• dual: مشكلتان = two problems

This matches the meaning of the subject: two listed conditions.

Because مشكلتان is in the nominative dual form.

In this kind of sentence, the predicate is nominative, so the dual ending is:

• -تانِ for feminine dual nominative

Compare:

• مشكلتانِ = two problems (nominative)
• مشكلتَينِ = two problems (accusative/genitive)

So here مشكلتان is correct because it is the predicate of a nominal sentence.

Because the singular noun is مشكلة, and مشكلة is a feminine noun in Arabic.

So its dual is also feminine:

• مشكلة
• مشكلتان

This is about the gender of the noun مشكلة itself, not about whether the medical conditions are biologically feminine or anything like that. It is just normal grammatical gender.

Because both are the first word in an iḍāfa construction.

Here you have:

• تشوش الرؤية
• طول النظر

In a normal iḍāfa:

• the first noun usually does not take الـ
• the second noun determines whether the whole phrase is definite

So:

• تشوش الرؤية = disturbance/blurring of the vision
• طول النظر = longness of the sight / farsightedness

That is why you do not say التشوش الرؤية or الطول النظر here.

Yes, both are iḍāfa phrases.

• تشوش الرؤية literally means something like blurring/disturbance of vision
• طول النظر literally means longness of sight, which is the standard expression for farsightedness

So even if the medical meaning is already known, it helps to see how Arabic builds these phrases:

• noun + noun
• often understood in English as X of Y

Because Arabic often uses an indefinite predicate when it is classifying something.

So this sentence means:

• Blurred vision and farsightedness are two problems

not:

• Blurred vision and farsightedness are the two problems

If you said المشكلتان, it would sound more like you were referring to two specific, already known problems.

In a fully inflected reading, the cases are:

• تشوشُ — nominative
• الرؤيةِ — genitive
• طولُ — nominative
• النظرِ — genitive
• مشكلتانِ — nominative

Why?

• تشوش and طول are part of the subject, so they are nominative.
• الرؤية and النظر are the second term of iḍāfa, so they are genitive.
• مشكلتان is the predicate of a nominal sentence, so it is nominative.

In ordinary Arabic writing, these short vowel endings are usually not written, which is why learners often do not see them.

A fully vocalized version is:

تَشَوُّشُ الرُّؤْيَةِ وَطُولُ النَّظَرِ مُشْكِلَتَانِ

A careful, fully inflected pronunciation is roughly:

tashawwušu r-ruʾyati wa ṭūlu n-naẓari mushkilatāni

A few pronunciation notes:

• الرؤية is pronounced with ar-/r- because ر is a sun letter
• النظر is pronounced with an-/n- because ن is also a sun letter
• At the end of a sentence, many speakers pause and drop the final short vowel, so the pronunciation may sound a little shorter in natural speech