Mi prima abrió un nuevo negocio de repostería en el centro de la ciudad.

Prima means female cousin. Spanish usually marks this kind of family word for gender:

• prima = female cousin
• primo = male cousin

So the sentence tells you the cousin is female. English uses cousin for both, but Spanish normally does not.

In standard modern Spanish, possessive adjectives like mi, tu, su, nuestro usually go directly before the noun, without an article:

• mi prima
• tu casa
• su coche

So mi prima is the normal way to say my cousin. Using la mi prima would sound archaic or dialectal, not standard everyday Spanish.

Abrió is the third-person singular preterite of abrir.

• infinitive: abrir = to open
• abrió = he/she opened

It matches mi prima, which is she. The preterite is used because the sentence presents the opening of the business as a completed event in the past.

Because this sentence describes one completed action: your cousin opened the business.

• abrió = she opened it, completed event
• abría = she was opening / she used to open, more ongoing, repeated, or backgrounded

So abrió is the natural choice if you are simply reporting what happened.

Yes, it could be, depending on context.

In Spain, the present perfect is often used for a recent past action that still feels connected to the present:

• Mi prima ha abierto un nuevo negocio...

That can sound like My cousin has opened a new business...

But abrió is also perfectly correct. It simply tells the event as a finished past action, without emphasizing its present relevance in the same way.

Because negocio is a masculine noun:

• el negocio
• un negocio

The article and adjective must agree with the noun:

• un nuevo negocio

Even though some English speakers may focus on the ending, here the -o ending does match the usual masculine pattern.

In Spanish, adjectives can sometimes go before or after the noun, and the position can slightly change the nuance.

• un nuevo negocio usually means a new business in the ordinary sense: newly established, another business
• un negocio nuevo can sound more literal or contrastive: a business that is new, not old

In this sentence, un nuevo negocio is the most natural phrasing.

It can mean both, depending on context.

In Spanish, abrir un negocio is a very common way to say that someone started, set up, or launched a business. It is not limited to physically opening a door or opening for the day.

So here it means something like:

• she started a business
• she opened a business
• she launched a business

De repostería describes what kind of business it is.

Repostería refers to pastry-making, baking sweets, cakes, desserts, and similar products. So negocio de repostería means a business related to that field.

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

• tienda de ropa = clothing shop
• negocio de fotografía = photography business
• negocio de repostería = pastry/confectionery business

So de is the normal linking word here.

It is pronounced roughly re-pos-te-RI-a, with the stress on rí.

The accent mark shows where the stress goes:

• repostería

It also helps signal that í-a is pronounced in separate syllables, rather than being merged into one.

The accent mark shows that the stress falls on the final syllable:

• a-BRIÓ

Without the accent, the stress pattern would not be read the same way. In short, the accent helps show the correct pronunciation of this preterite form.

This is a very common Spanish location phrase:

• en = in
• el centro = the centre / downtown area
• de la ciudad = of the city

So the structure literally means in the centre of the city.

Spanish often uses el centro de la ciudad where English might simply say downtown or in the city centre.

Yes, if the context already makes it clear which place you mean.

• Mi prima abrió un nuevo negocio de repostería en el centro.

That can work if everyone already knows you mean the town or city centre. Adding de la ciudad makes it more explicit and complete.