Пусть шёлк и красивый, я всё равно выберу блузку из хлопка.

Here пусть does not mean a command like let in let him go.

In this sentence, пусть introduces a concession:
granted that, even if, although, admittedly.

So Пусть шёлк и красивый... means something like:

• Silk may be beautiful...
• Granted, silk is beautiful...
• Even if silk is beautiful...

This use of пусть is quite common in written and careful spoken Russian.

Not really. In this pattern, и is part of a concessive structure and often is not translated as a separate and.

The pattern is:

Пусть / хоть X и Y, ...

It means:

• although X is Y
• granted that X is Y
• X may be Y, but...

So Пусть шёлк и красивый, я всё равно... is basically:

Although silk is beautiful, I still...

The и helps strengthen the contrast, but in English it usually disappears in translation.

Because in Russian, the verb to be is normally omitted in the present tense.

So:

• шёлк красивый = silk is beautiful
• literally, Russian just says silk beautiful

This is completely normal. Russian only uses forms of быть more visibly in past and future, or in special contexts.

Because it agrees with шёлк.

Шёлк is:

• masculine
• singular
• nominative

So the adjective must match it:

• красивый = masculine singular nominative

If the noun were feminine, you would get красивая.
If it were neuter, красивое.
If plural, красивые.

Yes, красив is possible, but it sounds a bit more literary or formal.

Compare:

• шёлк красивый — very natural, neutral
• шёлк красив — also correct, but more bookish or stylistically marked

In modern everyday Russian, full adjective forms like красивый are very common in predicate position, especially in speech.

So this sentence is perfectly fine as written.

Because шёлк is the subject of the clause шёлк ... красивый.

It is the thing being described as beautiful, so nominative is exactly what you would expect.

Also, Russian often uses a bare singular noun to talk about something in general:

• Шёлк красивый = Silk is beautiful
• no article is needed, because Russian has no a / the

Because it is the direct object of выберу.

The verb выбрать means to choose, and what you choose goes in the accusative case.

So:

• я выберу блузку = I will choose a blouse

Since блузка is feminine and animate/inanimate rules matter, the accusative singular here is:

• nominative: блузка
• accusative: блузку

Выберу is the future tense of the perfective verb выбрать.

Perfective usually focuses on a completed result:

• выберу = I will choose / I will make the choice

That fits well here, because the speaker is talking about a final decision.

Compare:

• выберу — I will choose, I’ll settle on
• буду выбирать — I will be choosing, I’ll be in the process of choosing
• выбираю — I choose / I am choosing

In this sentence, выберу is the most natural form for I’ll choose.

Всё равно means:

• all the same
• anyway
• still
• nevertheless

It emphasizes that the speaker’s decision does not change, despite the concession in the first part.

So the logic is:

• Yes, silk is beautiful
• but even so, I will still choose a cotton blouse

That is exactly the job of всё равно here.

Because the preposition из normally requires the genitive case.

So:

• хлопок = cotton
• after из it becomes из хлопка = made of cotton / from cotton

This is a very common way to describe material:

• стол из дерева = a table made of wood
• кольцо из золота = a ring made of gold
• блузка из хлопка = a blouse made of cotton

Yes. Both are natural, but they are slightly different in form.

• блузку из хлопка = a blouse made of cotton
• хлопковую блузку = a cotton blouse

The second version uses the adjective хлопковый.
The first version uses a noun phrase with из.

Both are correct. In many everyday situations, хлопковую блузку may sound a little more compact and idiomatic, but блузку из хлопка is also completely normal.

Yes. The comma is needed because the sentence has two parts:

• concessive part: Пусть шёлк и красивый
• main part: я всё равно выберу блузку из хлопка

Russian separates this kind of introductory concessive clause from the main clause with a comma.

The sentence is understandable and grammatical. A native speaker might also say it in one of these ways:

• Пусть шёлк и красив, я всё равно выберу хлопковую блузку.
• Хоть шёлк и красивый, я всё равно выберу блузку из хлопка.
• Шёлк, конечно, красивый, но я всё равно выберу блузку из хлопка.

A few notes:

• хоть is another common concessive word, often very natural in speech
• красив sounds a bit more literary than красивый
• хлопковую блузку is a slightly more compact way to say a cotton blouse

So the original sentence is fine, but there are several very natural variants depending on style.