Эта блузка из такого мягкого хлопка, что в ней удобно даже в жару.

Because блузка is a feminine noun, so the demonstrative этот has to agree with it:

• masculine: этот
• feminine: эта
• neuter: это
• plural: эти

So:

• эта блузка = this blouse

Russian adjectives and pronouns must match the noun in gender, number, and case.

The preposition из usually means from / out of, and with materials it often means made of.

So:

• блузка из хлопка = a blouse made of cotton

This is a very common pattern in Russian:

• стол из дерева = a table made of wood
• кольцо из золота = a ring made of gold
• платье из шелка = a dress made of silk

Also, из requires the genitive case, which is why хлопок becomes хлопка.

Because they all depend on из, which requires the genitive case.

The base forms are:

• такой = such
• мягкий = soft
• хлопок = cotton

After из, they become genitive singular masculine:

• из такого мягкого хлопка

So all three words agree grammatically:

• такого matches хлопка
• мягкого matches хлопка
• хлопка is genitive because of из

In other words, Russian is saying:

• out of such soft cotton

This is the Russian equivalent of such ... that ....

So:

• из такого мягкого хлопка, что ...
• literally: made of such soft cotton that ...

The idea is:

1. first clause: describe the quality strongly
2. second clause: give the result

Compare:

• Он был такой уставший, что сразу уснул.
  = He was so tired that he fell asleep immediately.

• Это была такая трудная задача, что никто не решил её быстро.
  = It was such a difficult task that nobody solved it quickly.

In your sentence, такого is not nominative такой because it has to match хлопка in the genitive after из.

Because the sentence is not saying that the blouse itself feels soft in a simple direct way. It is specifically talking about the material:

• Эта блузка из такого мягкого хлопка...
• This blouse is made of such soft cotton...

If you said:

• Эта блузка такая мягкая

that would mean:

• This blouse is so soft

That is also possible Russian, but it shifts the focus. The original sentence emphasizes the cotton as the reason for the comfort.

Yes, literally в ней can mean in her or in it, depending on the noun. Here it refers to блузка, which is feminine, so:

• в ней = in it

With clothing, Russian often uses в + prepositional to mean wearing it / when you are in it:

• В этом пальто тепло. = It’s warm in this coat.
• В этих туфлях неудобно ходить. = It’s uncomfortable to walk in these shoes.
• В ней удобно. = It’s comfortable in it / It’s comfortable to wear.

So this is a very natural way to talk about clothing in Russian.

Because those two expressions are similar but not exactly the same.

• она удобная = it is comfortable / convenient as a thing
• в ней удобно = it is comfortable to be/walk/sit in it, especially when wearing it

For clothes, в ней удобно is often more idiomatic because it describes the experience of wearing the item.

Compare:

• Эта обувь удобная. = These shoes are comfortable.
• В этой обуви удобно ходить. = It’s comfortable to walk in these shoes.

In your sentence, в ней удобно fits especially well because the next part is даже в жару — it describes how it feels to wear the blouse in hot weather.

Because удобно here is not an adjective agreeing with блузка. It is used in an impersonal construction meaning:

• it is comfortable
• it feels comfortable
• one is comfortable in it

So:

• В ней удобно = It’s comfortable in it

If you used удобная, that would be an adjective directly describing the blouse:

• Блузка удобная. = The blouse is comfortable.

Both are possible in Russian, but they are structured differently:

• блузка удобная → the blouse is comfortable
• в блузке удобно → it is comfortable in the blouse

Because в жару is an idiomatic expression meaning in hot weather / in the heat.

The noun жара becomes жару here, which is the accusative singular. Russian often uses the accusative in expressions of time or conditions like this.

So:

• в жару = in the heat / during hot weather

This is just the normal expression to learn as a chunk.

Other similar expressions:

• в дождь = in the rain
• в холод = in the cold
• в мороз = in the frost / in freezing weather

So даже в жару means:

• even in hot weather
• even when it’s hot

Даже means even. It adds emphasis and suggests that the statement is true in a situation where you might not expect it to be true.

So:

• в ней удобно даже в жару

means:

• it’s comfortable in it even in the heat

The implication is that hot weather usually makes clothing less comfortable, but this blouse is still comfortable anyway.

Because что introduces a subordinate clause here.

The structure is:

• Эта блузка из такого мягкого хлопка, что ...

The part after что explains the result of the soft cotton. Russian normally separates this kind of subordinate clause with a comma.

Very similar examples:

• Он так устал, что не мог говорить.
• Было так холодно, что мы ушли домой.

So the comma is required.

Yes, Russian word order is flexible, though the original version is very natural.

Original:

• Эта блузка из такого мягкого хлопка, что в ней удобно даже в жару.

You might also hear:

• Эта блузка из такого мягкого хлопка, что даже в жару в ней удобно.

Both are understandable. The difference is mostly in emphasis:

• в ней удобно даже в жару emphasizes even in the heat
• даже в жару в ней удобно brings even in the heat forward a bit more

The original sentence sounds smooth and neutral.

Yes. Хлопок here is a material noun, like cotton in English. It is treated as a mass/material, not as individual countable items.

So:

• из хлопка = made of cotton

This is why singular is used. Russian does have plural forms of many material nouns in special contexts, but here the singular is the normal choice.

A fairly literal breakdown would be:

• Эта блузка = this blouse
• из такого мягкого хлопка = is made of such soft cotton
• что = that
• в ней удобно = it is comfortable in it / it is comfortable to wear
• даже в жару = even in the heat

So the whole sentence is roughly:

• This blouse is made of such soft cotton that it’s comfortable to wear even in hot weather.

That is a very natural Russian sentence, and the main grammar points are:

• agreement: эта
• из + genitive
• такой ..., что ... result structure
• impersonal удобно
• clothing expression в ней
• idiomatic в жару