En la papelería de la universidad también hay una fotocopiadora cerca de la puerta.

En means in or at, so En la papelería means in the stationery shop or at the campus stationery shop.

Spanish often begins a sentence with the place where something is located. So:

• En la papelería de la universidad... = In the university stationery shop...

If you removed en, you would no longer be saying where something is.

In Spain, papelería usually means a stationery shop or store that sells paper, school supplies, pens, notebooks, etc. It can sometimes also offer services like printing or photocopying.

So in this sentence, it refers to a place on campus where students might buy supplies and use a photocopier.

De la universidad literally means of the university or belonging to the university.

Spanish often uses de + noun where English might use a noun as an adjective:

• la biblioteca de la universidad = the university library
• la cafetería de la universidad = the university cafeteria
• la papelería de la universidad = the university stationery shop

You could sometimes use an adjective like universitaria, but here de la universidad is the most natural way to identify which stationery shop it is.

También means also or too. In this sentence it modifies the whole idea that there is a photocopier there.

So:

• también hay = there is also

This is a very common position for también in Spanish. It often goes before the verb:

• También tengo hambre. = I’m hungry too.
• También hay una impresora. = There is also a printer.

Other positions are sometimes possible, but también hay is the most natural here.

This is one of the most important Spanish differences for English speakers.

Use hay when you mean there is / there are and you are introducing the existence of something.

• Hay una fotocopiadora. = There is a photocopier.

Use está when the thing is already identified and you are saying where it is.

• La fotocopiadora está cerca de la puerta. = The photocopier is near the door.

So in your sentence, the speaker is first introducing the machine, so hay is correct.

Because the sentence is introducing a photocopier, not referring to one already known.

• una fotocopiadora = a photocopier
• la fotocopiadora = the photocopier

With hay, Spanish very often uses an indefinite article when mentioning something for the first time:

• Hay un profesor en el aula.
• Hay una mesa junto a la ventana.

If both speaker and listener already knew exactly which photocopier was being discussed, then la fotocopiadora might be possible in a different kind of sentence, but not usually with hay.

Cerca de means near or close to.

It is a fixed expression in Spanish, and it always needs de before the thing or place:

• cerca de la puerta = near the door
• cerca del aula = near the classroom
• cerca de aquí = near here

English speakers often want to say just cerca la puerta, but that is incorrect. You need de.

In Spanish, when talking about a specific, identifiable object like the door of that shop, the definite article is normally used.

So:

• cerca de la puerta = near the door

Spanish uses articles more often than English in these everyday location phrases. The door is understood to be the relevant one in that place.

Yes, Spanish word order is flexible, though some versions sound more natural than others.

The original sentence:

• En la papelería de la universidad también hay una fotocopiadora cerca de la puerta.

Other possible versions:

• También hay una fotocopiadora cerca de la puerta en la papelería de la universidad.
• Hay también una fotocopiadora cerca de la puerta en la papelería de la universidad.

The original sounds very natural because it starts with the location, then gives the new information.

Yes. Fotocopiadora is the normal word for photocopier or copy machine in Spain.

You may also hear related words:

• hacer fotocopias = to make photocopies
• una fotocopia = a photocopy

So:

• Hay una fotocopiadora. = There’s a photocopier.
• Necesito hacer una fotocopia. = I need to make a photocopy.

You would change una fotocopiadora to the plural, and hay would stay the same.

• En la papelería de la universidad también hay fotocopiadoras cerca de la puerta.
• En la papelería de la universidad también hay unas fotocopiadoras cerca de la puerta.

Notes:

• hay works for both singular and plural.
• fotocopiadoras = photocopiers
• Often Spanish omits the article in plural after hay unless you want to make it sound less indefinite.

Hay is pronounced roughly like eye in English.

It comes from the verb haber, but in this use it is an impersonal form meaning there is / there are.

Important points:

• hay = present tense
• it does not change for singular or plural
• it is used only to express existence

Examples:

• Hay un libro. = There is a book.
• Hay dos libros. = There are two books.

Yes, it sounds natural. It is a normal descriptive sentence giving location information.

A native speaker might also say close variants such as:

• En la papelería de la universidad también hay una fotocopiadora, cerca de la puerta.
• También hay una fotocopiadora cerca de la puerta, en la papelería de la universidad.

But the original sentence is perfectly good, clear Spanish.