El domingo vamos a comer paella con mis primas en casa de mi abuela.

Yes. In Spanish, el + day of the week often means on that day.

So:

• El domingo = on Sunday
• El lunes = on Monday

This is a very common structure in Spanish. English uses on, but Spanish usually uses the definite article el instead.

Examples:

• El sábado trabajo. = I work on Saturday.
• El martes tenemos clase. = We have class on Tuesday.

It usually means this Sunday / next Sunday, depending on context.

In a sentence like:

• El domingo vamos a comer paella...

most people will understand it as a specific upcoming Sunday.

If you want to speak about Sundays in general, Spanish often uses:

• Los domingos = On Sundays

For example:

• Los domingos comemos en casa de mi abuela. = On Sundays we eat at my grandmother’s house.

So here, El domingo is most naturally understood as one particular Sunday.

Vamos a + infinitive is a very common way to talk about the near future in Spanish.

So:

• vamos a comer = we are going to eat

This is similar to English be going to + verb.

You could also say:

• Comeremos paella = We will eat paella

That is correct too, but vamos a comer often sounds more natural in everyday conversation when talking about plans.

Compare:

• Vamos a comer paella = We’re going to eat paella
• Comeremos paella = We will eat paella

Both work, but the first is especially common in spoken Spanish.

Because Spanish usually leaves out subject pronouns when they are not needed.

The verb form vamos already tells you the subject is we.

So:

• (Nosotros) vamos a comer paella

Both are possible, but nosotros is often omitted because it is understood from the verb.

Spanish does this a lot:

• Tengo hambre. = I am hungry.
• Vivimos en Madrid. = We live in Madrid.

You only add the pronoun for emphasis, contrast, or clarity.

Because after verbs like comer, Spanish often uses food words without an article when speaking generally about what someone is eating.

So:

• comer paella = to eat paella
• beber agua = to drink water
• comprar pan = to buy bread

If you say la paella, it usually sounds more specific, as if you mean a particular paella.

Compare:

• Vamos a comer paella. = We’re going to eat paella.
• Vamos a comer la paella. = We’re going to eat the paella.
  (a specific one)

Primas means female cousins.

Spanish nouns show both number and gender:

• prima = female cousin
• primas = female cousins
• primo = male cousin
• primos = male cousins / cousins in a mixed group

And mis means my.

So:

• mis primas = my female cousins

This tells you the speaker’s cousins are female.

Because con is the normal Spanish word for with when you mean being together with someone.

So:

• con mis primas = with my cousins

Examples:

• Voy con mi hermano. = I’m going with my brother.
• Estudio con mis amigos. = I study with my friends.

It is a very direct match with English with in this kind of sentence.

Because en casa de... means at the house/home of..., which in natural English is usually at my grandmother’s house or at my grandmother’s place.

So:

• en casa de mi abuela = at my grandmother’s house

By contrast, a casa de... usually expresses movement to someone’s house:

• Vamos a casa de mi abuela. = We’re going to my grandmother’s house.

So the difference is:

• en casa de mi abuela = at my grandmother’s house
• a casa de mi abuela = to my grandmother’s house

In your sentence, the idea is where the meal will happen, so en is the right preposition.

Spanish often uses en casa de + person as a fixed expression meaning at someone’s house/home.

So:

• en casa de mi abuela = at my grandmother’s house
• en casa de Ana = at Ana’s house

You can say en la casa de mi abuela, but it sounds more literal and physical, like referring to the building itself. En casa de... is the more natural everyday expression when talking about being at someone’s home.

Because Spanish does not use the article la before a possessive like mi in standard modern Spanish.

So you say:

• mi abuela = my grandmother
• mi casa = my house
• mis primas = my cousins

Not:

• la mi abuela
• la mi casa

English and Spanish are similar here: both normally use just the possessive word.

Yes. That would also be correct.

Spanish word order is often more flexible than English, especially with time, place, and company phrases.

Your original sentence:

• El domingo vamos a comer paella con mis primas en casa de mi abuela.

A possible variation:

• El domingo vamos a comer paella en casa de mi abuela con mis primas.

Both are grammatical. The difference is mostly about emphasis or rhythm:

• con mis primas first highlights who you are eating with
• en casa de mi abuela first highlights where it will happen

So the original sentence is natural, but it is not the only possible order.

Because in Spanish, days of the week are normally written in lower case.

So:

• lunes
• martes
• domingo

This is different from English, where we write Sunday, Monday, and so on with capital letters.

In your sentence, El is capitalized only because it is the first word of the sentence, not because domingo is a proper noun.