Я не люблю высокие каблуки, поэтому всегда смотрю, какая у обуви ткань внутри.

Yes — in Russian, каблуки can stand for high-heeled shoes in a general way, much like English can sometimes use heels.

So Я не люблю высокие каблуки means:

• I don’t like high heels
• more literally: I don’t like high heels / high-heeled footwear

Russian often uses каблуки this way without naming the shoes themselves.

Because каблуки is:

• plural
• inanimate
• here it is the direct object of люблю

With любить, the object normally goes in the accusative case. But for inanimate plural nouns, the accusative looks the same as the nominative.

So:

• nominative plural: высокие каблуки
• accusative plural: высокие каблуки

That is why the adjective is высокие and the noun is каблуки.

In Russian, не normally goes directly before the verb it negates.

So:

• люблю = I love / like
• не люблю = I do not love / like

Люблю не would sound incomplete or unnatural unless something special followed it for contrast.

Поэтому means therefore, so, or that’s why.

In this sentence it links the first idea to the result:

• I don’t like high heels, so I always check...

It often appears after a comma between two clauses:

• ..., поэтому ...

That is a very common and natural position.

Because смотреть means to look, to watch, or to check by looking, while видеть means to see.

Here the speaker means:

• I always look/check what the inside material is not
• I always see...

So смотрю is the natural choice because it emphasizes the action of examining something.

Because какая here is not a direct object. It belongs to the subordinate clause and describes ткань, which is the subject of that clause.

The structure is roughly:

• смотрю, какая ... ткань ...
• I look/check what kind of fabric ... is ...

Inside that clause:

• ткань = fabric, nominative feminine singular
• какая agrees with ткань

So we get:

• какая ткань = what kind of fabric

If it were a direct object, then какую might be needed, but that is not the grammar here.

У + genitive is a very common Russian way to express possession or something like something belonging to / associated with something.

So:

• у обуви ткань внутри literally means something like the shoes have fabric inside or there is such-and-such fabric inside the footwear

More natural English would be:

• what material the inside of the shoe is
• what fabric the shoes have inside
• what the lining is made of

So у обуви is not really at the shoes here. It is a possession-type structure.

Because after у, Russian uses the genitive case.

The noun is:

• dictionary form: обувь = footwear, shoes

Genitive singular:

• обуви

So:

• у обуви = of the footwear / the shoes have

Also, обувь is usually treated as a singular collective noun in Russian, even though in English we often say shoes in the plural.

Usually обувь means footwear in a general sense.

It is a collective noun, so Russian often uses it where English would say:

• shoes
• footwear

In this sentence, it refers generally to the shoes being considered, not to one single shoe.

Literally, yes: fabric inside.

But in natural English, this often refers to:

• the inner material
• the lining
• the material on the inside of the shoe

So the sentence is not necessarily about fabric in a technical textile sense only; it is about what the inside surface/material is.

Внутри means inside.

Russian word order is flexible, and putting внутри at the end is natural here. It highlights the location being discussed:

• what kind of fabric the shoes have inside

You could sometimes see similar ideas expressed differently, such as:

• какая внутри обуви ткань
• какая ткань внутри обуви

But the original sentence sounds natural and conversational.

No. It is an indirect question inside a larger sentence.

The main clause is:

• Я ... всегда смотрю = I always look/check

What the speaker is checking is expressed by the indirect question:

• какая у обуви ткань внутри = what kind of fabric is inside the shoes

So there is no question mark, and the word order stays normal for a subordinate clause.

Yes. A natural English translation might be:

• I don’t like high heels, so I always check what the inside of the shoes is made of.
• I don’t like high heels, so I always look at what material the inside is.
• I don’t like high heels, so I always check the lining material.

A very literal translation is useful for grammar, but a more natural translation often sounds smoother in English.