Barajamos la baraja y preparamos el mazo.

They can be either one, depending on context.

For regular -ar verbs, the nosotros form is the same in:

• the present indicative: we shuffle / we prepare
• the preterite: we shuffled / we prepared

So:

• barajamos = we shuffle or we shuffled
• preparamos = we prepare or we prepared

In an isolated textbook sentence, learners are often meant to read it as present unless the wider context makes it clearly past.

Because Spanish often drops subject pronouns.

The verb ending already tells you who is doing the action:

• -amos = we for these forms

So Barajamos la baraja... already means We shuffle the deck... without needing nosotros.

You could add nosotros if you want emphasis, contrast, or clarity:

• Nosotros barajamos la baraja y preparamos el mazo.

But most of the time, it is not necessary.

Yes. They come from the same root:

• barajar = to shuffle
• baraja = deck of cards

So barajamos la baraja uses a verb and a noun that are closely related.

That kind of repetition is perfectly possible in Spanish. It may feel a bit repetitive to an English speaker, but it is grammatical.

It is grammatical and understandable, but it can sound a little repetitive because barajar already strongly suggests cards.

Depending on context, a native speaker might also say:

• Barajamos.
• Barajamos las cartas.

Still, barajamos la baraja is not wrong. It can be used when the speaker wants to mention the deck explicitly.

Both can refer to cards, but they are not always exactly the same.

• la baraja usually means the deck of cards
• el mazo often means the pack/stack/pile of cards, especially the physical pile used in a game

In real usage, the exact nuance depends on the game and the situation. In some contexts they can overlap, but they are not always perfect synonyms.

Also, mazo has other meanings in Spanish, but in this sentence it is clearly about cards.

Spanish normally uses the definite article with specific nouns like these:

• la baraja
• el mazo

So the sentence is talking about the deck and the pack/pile, not just any deck or any pack.

The articles also show the nouns’ grammatical gender:

• la baraja = feminine
• el mazo = masculine

Because each word refers to the whole set as one unit.

This is similar to English:

• the deck
• the pack
• the pile

Even though a deck contains many cards, the noun itself is singular, so Spanish uses:

• la baraja
• el mazo

not plural forms.

No.

The personal a is mainly used before specific people (and sometimes pets or personified beings). Here, the objects are things:

• la baraja
• el mazo

So there is no personal a:

• Barajamos la baraja
• preparamos el mazo

not a la baraja or al mazo.

Yes, people would understand it, but it is not the most idiomatic choice for cards.

• mezclar = to mix
• barajar = to shuffle

For cards, barajar is the normal and more natural verb in Spanish.
So:

• Barajamos la baraja sounds more card-specific.
• Mezclamos las cartas is understandable, but more general.

A few key points:

• j in barajamos and baraja is a strong throaty sound, like the ch in Scottish loch or German Bach
• z in most of Spain is pronounced like th in think

So roughly:

• baraja ≈ ba-RA-ja with a throaty j
• barajamos ≈ ba-ra-JA-mos
• mazo ≈ MA-tho in most of Spain

In much of Latin America, and also in some parts of Spain, z is pronounced like s, so mazo may sound more like MA-so.

Because the normal word for and is y.

It only changes to e before a word that begins with an i sound:

• padre e hijo
• España e Italia

But preparamos starts with p, so the conjunction stays y:

• Barajamos la baraja y preparamos el mazo.