कमीज़ और पैंट अलग हैं।

Because the subject is compound: कमीज़ और पैंट = shirt and pants.
When two things are joined by और (and), Hindi usually treats them as plural, so you use हैं rather than है.

• कमीज़ अलग है। = The shirt is separate/different.
• पैंट अलग है। = The pants/trousers item is separate/different.
• कमीज़ और पैंट अलग हैं। = The shirt and pants are separate/different.

और means and.

It joins the two nouns:

• कमीज़ = shirt
• पैंट = pants/trousers
• कमीज़ और पैंट = shirt and pants

अलग means separate, different, or apart, depending on context.

In this sentence, it most naturally means that the shirt and the pants are separate items or not together / not matching as one set.

So the sentence could imply things like:

• they are kept separately
• they are not part of the same set
• they are different from each other

Context decides the best English wording.

Usually, अलग does not change form. It behaves like an indeclinable adjective in normal usage.

So you can say:

• लड़का अलग है।
• लड़की अलग है।
• लड़के अलग हैं।
• कमीज़ और पैंट अलग हैं।

The word अलग stays the same.

Both कमीज़ and पैंट are generally treated as feminine nouns in Hindi.

Examples:

• यह कमीज़ नई है।
• यह पैंट नई है।

But in your sentence, the important thing is not the individual gender of each noun. Since कमीज़ और पैंट together form a plural subject, the verb becomes हैं.

Hindi usually prefers Subject + complement + verb word order, with the verb often coming near the end.

So:

• कमीज़ और पैंट = subject
• अलग = complement/adjective
• हैं = are

That gives:

कमीज़ और पैंट अलग हैं।

This is very normal Hindi sentence structure.

Hindi does not have articles like a, an, and the in the same way English does.

So कमीज़ और पैंट can mean:

• shirt and pants
• the shirt and the pants
• a shirt and pants

The exact meaning depends on context.

They are both commonly used in Hindi, but they come from other languages.

• कमीज़ ultimately comes through Persian/Arabic usage and means shirt
• पैंट is a borrowing from English pant/pants

This is very common in Hindi. Everyday Hindi includes many borrowed words, especially for clothing and modern objects.

Yes. अलग-अलग is also very common.

Difference in nuance:

• अलग हैं = are separate / are different
• अलग-अलग हैं = are separate from each other / are individually separate

In many situations, both are natural.
अलग-अलग adds a bit more emphasis.

In Hindi, पैंट is usually treated as a single noun referring to one pair of trousers/pants.

So you can say:

• यह पैंट नई है। = These pants / this pair of pants is new.

Even though English uses a plural form pants, Hindi commonly treats पैंट as one item.
In your sentence, the plural verb हैं is not because of पैंट alone; it is because कमीज़ और पैंट together make a plural subject.