Prefiero enviar el documento por correo electrónico.

In Spanish, subject pronouns are often omitted because the verb ending already shows who is doing the action.

• Prefiero = I prefer
• The -o ending tells you it is I

So Prefiero enviar el documento... is completely natural.
You could say Yo prefiero..., but that usually adds emphasis or contrast, for example:

• Yo prefiero enviar el documento, no imprimirlo.
  = I prefer to send the document, not print it.

Because preferir is a stem-changing verb. In the present tense, the e in the stem changes to ie in most forms.

So:

• yo prefiero
• tú prefieres
• él/ella prefiere
• nosotros preferimos
• vosotros preferís
• ellos prefieren

This is a very common pattern in Spanish.
The infinitive is preferir, but the yo form is prefiero.

After verbs like preferir, querer, necesitar, and decidir, Spanish often uses a second verb in the infinitive.

So:

• Prefiero enviar = I prefer to send
• Quiero comer = I want to eat
• Necesito estudiar = I need to study

This is similar to English prefer to send.

Spanish often uses the definite article more regularly than English.

• el documento = the document

In this sentence, it refers to a specific document, so el is natural.

If you said un documento, that would mean a document, which is less specific.

Compare:

• Prefiero enviar el documento = I prefer to send the document
• Prefiero enviar un documento = I prefer to send a document

Here, por means by or via, showing the method used to send something.

• por correo electrónico = by email
• por teléfono = by phone
• por internet = via the internet

This is a very common use of por: expressing means or medium.

Correo by itself usually means mail/post in a general or traditional sense.

• correo = mail/post
• correo electrónico = email

So:

• por correo = by post / by mail
• por correo electrónico = by email

In everyday Spanish, people also often shorten correo electrónico to just email or correo, depending on context, but correo electrónico is the full, clear version.

Yes. Mandar and enviar can both mean to send.

• enviar sounds a bit more neutral or formal
• mandar is very common in everyday speech

So both are correct:

• Prefiero enviar el documento por correo electrónico
• Prefiero mandar el documento por correo electrónico

In many situations, they mean the same thing.

You would normally say por correo electrónico.

A través de means through or by means of, but with email, por correo electrónico is the standard and most natural expression.

So:

• natural: enviar el documento por correo electrónico
• less natural here: enviar el documento a través de correo electrónico

If you do use a través de, you would more naturally say:

• a través del correo electrónico

But even then, por correo electrónico is still the most common choice.

Because in Spanish, when one verb is followed by an infinitive, the infinitive usually comes directly after the first verb.

So the structure is:

• Prefiero + infinitive + object
• Prefiero enviar el documento

This is the normal order.

Prefiero el documento enviar sounds incorrect because el documento interrupts the verb pattern in an unnatural way.

No. It is masculine because the main noun is correo, which is masculine: el correo.

The adjective electrónico must agree with correo, so it also appears in the masculine singular form:

• el correo electrónico

If the noun were feminine, the adjective would change too. For example:

• la dirección electrónica

So the gender comes from the noun, not from the adjective.

The sentence is natural in both Spain and Latin America.

In Spain, correo electrónico is fully standard, though people also say email in casual speech.

A few possible regional differences:

• Spain: mandar is very common for send
• Latin America: enviar is also very common everywhere
• Casual speech in many places: por email may be heard instead of por correo electrónico

But your original sentence is correct and clear in Spain.

You can simply raise your intonation in speech, or use question marks in writing:

• ¿Prefieres enviar el documento por correo electrónico?
  = Do you prefer to send the document by email?

Notice that for you, the verb changes:

• prefieres = you prefer

If you wanted to ask Do I prefer to send the document by email?, that would be unusual unless you were thinking aloud:

• ¿Prefiero enviar el documento por correo electrónico?