Эта ткань мягкая, но ремешок у сумочки слишком короткий, и мне это не нравится.

In Russian, the verb to be is usually omitted in the present tense.

So:

• Эта ткань мягкая = This fabric is soft
• ремешок ... слишком короткий = the strap ... is too short

Russian does this very often in the present tense. If you wanted past or future, then a form of быть would appear:

• Эта ткань была мягкая = This fabric was soft
• Ремешок будет короткий = The strap will be short

So the lack of is here is completely normal.

Because ткань is a feminine noun in Russian, even though it ends in ь.

The demonstrative this must agree with the noun in gender, number, and case:

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

So:

• эта ткань = this fabric
• этот ремешок = this strap
• это платье = this dress
• эти сумочки = these handbags

A common learner difficulty is that nouns ending in ь can be either masculine or feminine, so you often just have to learn the gender with the word.

Because adjectives in Russian must agree with the nouns they describe.

Here:

• ткань is feminine singular nominative, so soft becomes мягкая
• ремешок is masculine singular nominative, so short becomes короткий

Compare:

• мягкая ткань = soft fabric
• мягкий материал = soft material
• мягкое кресло = soft armchair
• мягкие вещи = soft things

And:

• короткий ремешок = short strap
• короткая юбка = short skirt
• короткое письмо = short letter
• короткие волосы = short hair

So the endings change because the nouns are different.

У сумочки literally means something like at the little bag/handbag, but in Russian this structure is very often used to show possession.

So:

• ремешок у сумочки = the strap of the handbag / the handbag’s strap

This is a very common Russian pattern:

• ручка у двери = the handle of the door
• крыша у дома = the roof of the house
• глаза у ребёнка = the child’s eyes

It is often more natural in Russian than forcing a direct equivalent of English of.

Because after у, the noun normally goes into the genitive case.

The dictionary form is:

• сумочка = handbag, little bag

After у, it becomes:

• у сумочки

So this is not a different word entirely; it is the same noun in a different case.

Also, note that сумочка itself is a diminutive form of сумка. It often sounds more like handbag, small bag, or just a slightly more affectionate/everyday version depending on context.

Both сумочка and ремешок are diminutive forms.

• сумка = bag

• сумочка = little bag / handbag / a more delicate or affectionate way to say bag

• ремень = strap, belt
• ремешок = little strap / a smaller or more specific strap

Diminutives in Russian can express:

• small size
• affection
• informality
• a more natural everyday label for certain objects

In this sentence, сумочка and ремешок do not necessarily mean the speaker is being emotional or cute; they may simply be the most natural words for handbag and its strap.

Слишком means too in the sense of more than is good/acceptable/desired.

So:

• слишком короткий = too short

This is different from очень, which means very:

• очень короткий = very short
• слишком короткий = too short

The second one implies a problem. In this sentence, the strap is not just short; it is undesirably short.

Because нравиться works differently from English to like.

Russian treats the thing liked as the grammatical subject, and the person who experiences the feeling is put in the dative case.

So:

• мне это нравится = this is pleasing to me = I like this
• мне это не нравится = this is not pleasing to me = I don’t like this

Here:

• мне = to me
• это = this/it
• не нравится = does not please

This structure is very common:

• Мне нравится музыка = I like music
• Ей нравится книга = She likes the book
• Нам не нравится фильм = We don’t like the film

Because the grammatical subject here is это, which is singular.

• Это мне не нравится / Мне это не нравится = I don’t like this

Since это is singular, the verb is singular:

• нравится

If the subject were plural, you would use нравятся:

• Мне нравятся эти туфли = I like these shoes
• Мне не нравятся эти ремешки = I don’t like these straps

So the verb agrees with the thing being liked, not with the person.

Here это most likely refers to the whole situation just mentioned, especially the fact that the strap is too short.

So мне это не нравится means something like:

• I don’t like that
• I don’t like this
• I don’t like it

In context, it can refer broadly to what was just said, not only to one noun.

Russian often uses это this way to sum up a previous statement.

Yes. Russian word order is more flexible than English word order, though different orders can shift emphasis.

For example:

• Мне это не нравится = neutral, very common
• Это мне не нравится = emphasizes this
• Не нравится мне это = stronger emphasis, more expressive

In your sentence, и мне это не нравится sounds natural and neutral.

The earlier part is also fairly flexible, but the given order is smooth and standard:

• Эта ткань мягкая, но ремешок у сумочки слишком короткий...

Но means but and shows a stronger contrast or contradiction.

Here the speaker is saying:

• one thing is good: the fabric is soft
• another thing is bad: the strap is too short

So но fits well.

Could а appear in some similar sentences? Yes, but а usually marks contrast in a milder or more comparative way, not necessarily a contradiction.

For example:

• Ткань мягкая, а ремешок короткий = The fabric is soft, while/as for the strap, it is short

That sounds more like a contrast between two facts.
With но, the sentence more clearly suggests: however / but there is a problem.

They are in the nominative case because each is the subject of its clause:

• Эта ткань мягкая
• ремешок у сумочки слишком короткий

In Russian, the thing being described with an adjective in this kind of sentence is normally in the nominative.

So:

• ткань = nominative singular
• ремешок = nominative singular

Meanwhile, сумочки is not nominative, because it follows у and therefore appears in the genitive case.

It is a full adjective, not a short form.

• full form: мягкий, мягкая, мягкое, мягкие
• short form: мягок, мягка, мягко, мягки or similar literary/stylistic variants depending on the adjective

In modern everyday Russian, sentences like this normally use the full form:

• Ткань мягкая
• Ремешок короткий

That is completely standard.

Short-form adjectives do exist, but they often sound more formal, literary, or have slightly different usage depending on the adjective.