У этой сумочки короткий ремешок, а у той — длинный.

Russian very often expresses possession with the pattern:

У + possessor in the genitive + possessed thing

So:

• У этой сумочки короткий ремешок = literally At this handbag, there is a short strap
• Natural English translation: This handbag has a short strap

This у + genitive pattern is much more common in everyday Russian than using иметь (to have) for ordinary possession.

Because у requires the genitive case.

The base form is:

• эта сумочка = this little handbag

After у, it changes to genitive:

• у этой сумочки

Both words change because they are feminine singular:

• эта → этой
• сумочка → сумочки

The same thing happens in the second half:

• та → той

So у той means that one’s / by that one / that handbag has... depending on how you translate it.

Yes. Сумочка is a diminutive form of сумка.

• сумка = bag, handbag
• сумочка = little bag, handbag, purse; often sounds a bit more affectionate, lighter, or simply more natural for a small women’s bag

In many contexts, сумочка is just the normal word for a small handbag or purse, even if English would simply say bag or handbag.

Because ремешок is the thing being talked about as the possessed item.

In this pattern:

У + genitive possessor + nominative possessed thing

So:

• у этой сумочки = possessor
• короткий ремешок = what it has

That is why ремешок stays nominative singular, and the adjective agrees with it:

• ремешок — masculine singular nominative
• короткий — masculine singular nominative

Here а is best understood as a contrastive and or whereas.

So the sentence structure is:

• This handbag has a short strap, whereas that one has a long one

Russian а often links two things by contrast, even when the contrast is mild.

So in this sentence, а does not just add information; it sets up a comparison between the two handbags.

Because Russian often omits words that are obvious from context.

The full version would be:

• У этой сумочки короткий ремешок, а у той длинный ремешок.

But repeating ремешок is unnecessary, since it is already understood. So Russian leaves it out:

• а у той — длинный

English does the same thing:

• This one has a short strap, and that one a long one.

The missing noun is understood as ремешок.

The dash marks an omission: something has been left out because it is understood from the first part.

In effect, the second half means:

• а у той [ремешок] длинный or
• а у той [он] длинный

The dash helps the reader see the pause and understand that Russian is intentionally skipping repeated material.

In writing, this kind of dash is common when part of the sentence is omitted but clearly implied.

Russian does have short-form adjectives, but in modern everyday speech the full form is often more common in sentences like this.

So:

• ремешок короткий
• ремешок длинный

are completely normal.

Short forms like короток or длинен are possible in some contexts, but they can sound more formal, literary, or stylistically marked. For a simple everyday description of a handbag strap, the full forms короткий and длинный are the natural choice.

Yes, that is possible.

Russian word order is flexible, and changing it can shift emphasis slightly.

Compare:

• У этой сумочки короткий ремешок
  Neutral: This handbag has a short strap.

• У этой сумочки ремешок короткий
  Slightly more emphasis on the strap as the topic, then its quality

Both are grammatical. The original sentence sounds very natural and smooth for a contrast like short ... long.

Because сумочки is also omitted as unnecessary repetition.

The full version could be:

• а у той сумочки — длинный ремешок

But once сумочки has already appeared, Russian can shorten it to:

• а у той — длинный

Here той means that one and stands for той сумочки.

So in the second half, Russian is omitting both:

• сумочки
• ремешок

because both are clear from context.

Yes, very much so.

Although literally they come from this and that, in context they function like:

• у этой = this one has...
• у той = that one has...

More exactly, they stand for:

• у этой сумочки
• у той сумочки

So a good way to feel the sentence is:

• This handbag has a short strap, while that one has a long one.

That is a very natural English equivalent of what the Russian structure is doing.