В пенале у моей племянницы всегда есть маленькая точилка и ластик.

A very literal breakdown is:

В пенале — in the pencil case
у моей племянницы — of / with my niece, literally at my niece
всегда есть — there is always / there are always
маленькая точилка и ластик — a small sharpener and an eraser

So Russian is building the idea more like:

In the pencil case, with my niece, there is always a small sharpener and an eraser.

That sounds odd in English, but it is a normal Russian way to express location and possession together.

Because в can mean in, and when it shows location, it usually takes the Prepositional case.

The basic noun is пенал.
In the Prepositional singular, it becomes пенале.

So:

пенал → pencil case
в пенале → in the pencil case

If в showed motion into something, Russian would use the Accusative instead instead of the Prepositional.

This is a very common Russian possession pattern:

у + Genitive = at someone / with someone and very often someone has

So:

у моей племянницы literally means at my niece
but in context it helps express my niece’s

In this sentence, it helps create the idea of in my niece’s pencil case or in the pencil case that my niece has.

English usually uses my niece’s, but Russian very often prefers structures with у.

Because у requires the Genitive case.

The base form is:

моя племянница — my niece

After у, both words change to Genitive singular:

моей племянницы

The pronoun моей agrees with племянницы in case, number, and gender.

So the pattern is:

у + Genitive
у моей племянницы

Yes. That is also correct.

Compare:

в пенале моей племянницы — in my niece’s pencil case
в пенале у моей племянницы — also in my niece’s pencil case, with a slightly more conversational Russian feel

Both are natural. The version with у is very common in everyday Russian, especially when Russian wants to make the possessor feel more explicit.

Here есть means there is / there are in the sense of existence or presence.

So:

всегда есть = there is always / there are always

This is different from the fact that Russian often leaves out the present tense of to be in sentences like:

Она студентка — she is a student

In this sentence, есть is useful because the sentence is about something being present in a certain place.

Because they are in the Nominative case here.

In affirmative existential sentences with есть, the things that exist are often in the Nominative:

есть точилка
есть ластик

So:

маленькая точилка и ластик are the things that are present in the pencil case.

This is important because in negative sentences Russian often switches to the Genitive, for example:

нет ластика — there is no eraser

Because маленькая is feminine singular, so it agrees with точилка, which is feminine.

точилка — feminine
ластик — masculine

So маленькая точилка и ластик means:

a small sharpener and an eraser

It does not automatically mean that the eraser is small too.

If you want both items to be small, Russian usually repeats the adjective:

маленькая точилка и маленький ластик

In this use, present-tense есть does not change for singular vs. plural the way English changes is/are.

So Russian uses the same word:

есть книга — there is a book
есть книги — there are books

That is why есть works fine even though the sentence mentions two things.

Yes. Russian word order is flexible, although some orders sound more natural than others.

The given version starts with the location:

В пенале у моей племянницы всегда есть...

That feels natural because it sets the scene first.

You could also say:

У моей племянницы в пенале всегда есть маленькая точилка и ластик.

This is also natural. The meaning stays basically the same, but the emphasis shifts slightly.

Russian often uses word order to control focus, not just grammar.

Because Russian has no articles.

So Russian simply says:

маленькая точилка и ластик

and English decides from context whether to say:

a small sharpener and an eraser
or
the small sharpener and the eraser

In this sentence, English normally uses a/an because the objects are being mentioned as items present in the pencil case, not as already specifically identified objects.

Yes, it can be.

Russian пенал means pencil case or school supply case, not English penal.

So в пенале means in the pencil case, not anything related to punishment or law.

This is a good vocabulary item to memorize as a separate word.

There are two common possibilities.

If you mean not always, you keep есть:

В пенале у моей племянницы не всегда есть ластик.
My niece’s pencil case does not always have an eraser.

But if you mean there is no eraser, Russian often uses нет plus the Genitive:

В пенале у моей племянницы нет ластика.

Notice the change:

ластик → Nominative in the affirmative
ластика → Genitive after нет

That nominative/genitive contrast is very common in Russian existence sentences.