Mi papá compra algodón de azúcar.

In a normal statement, Spanish usually uses the possessive: mi papá = my dad.

Just papá is more often used when directly addressing him, like:

• Papá, ven aquí. = Dad, come here.

In your sentence, you are talking about him, not talking to him, so mi papá is the natural choice.

Both can mean father, but they are used differently:

• papá = dad, more personal and everyday
• padre = father, more formal or neutral

So Mi papá compra algodón de azúcar sounds warm and natural in everyday speech.
Mi padre compra algodón de azúcar is also correct, but it sounds a bit more formal.

Comprar is the infinitive, meaning to buy.
In a full sentence, you usually need a conjugated verb.

Here, compra is the third person singular form of comprar in the present tense:

• yo compro = I buy
• tú compras = you buy
• él/ella compra = he/she buys

Since mi papá is he, the correct form is compra.

In this sentence, compra most directly means buys.

Spanish present tense can sometimes also sound like is buying, depending on context, but the basic meaning is simply present tense:

• Mi papá compra algodón de azúcar. = My dad buys / is buying cotton candy.

If you specifically want to stress is buying right now, Spanish often uses:

• Mi papá está comprando algodón de azúcar.

Spanish often leaves out subject pronouns because the verb ending already shows who the subject is.

• compra already tells you it is he/she/you-formal
• and mi papá makes it completely clear who it is

So:

• Mi papá compra algodón de azúcar. is natural
• Él compra algodón de azúcar. is also possible, but here él is unnecessary

Spanish does this much more than English.

Because after compra, Spanish often uses the noun directly when talking about buying something in a general sense.

So:

• compra algodón de azúcar = buys cotton candy

Adding an article is possible in some contexts, but it changes the feel:

• compra el algodón de azúcar would sound more like buys the cotton candy, meaning specific cotton candy already known in the context

Without the article, it is just the normal way to say he is buying cotton candy.

Here de means of.

Literally, algodón de azúcar is cotton of sugar.
That is the Spanish expression for cotton candy.

This is very common in Spanish: a noun + de + another noun.

So even though the literal wording is different from English, the whole phrase works as one vocabulary item:

• algodón de azúcar = cotton candy

The accent mark in Spanish usually shows which syllable is stressed.

• papá is stressed on the last syllable: pa-PÁ
• mi has no written accent because it follows normal stress rules and does not need one here

Also, this mi is the possessive adjective meaning my.

Be careful not to confuse it with mí (with an accent), which means me after a preposition:

• mi papá = my dad
• para mí = for me

They have accent marks to show the correct stress:

• algodón → al-go-DÓN
• azúcar → a-ZÚ-car

Without those accents, a learner might stress the wrong syllable.

Spanish accent marks are very useful because they help both pronunciation and meaning.

A simple pronunciation guide for an English speaker would be:

• Mi ≈ mee
• papá ≈ pah-PAH
• compra ≈ KOHM-prah
• algodón ≈ ahl-goh-DON
• de ≈ deh
• azúcar ≈ ah-THOO-kar in most of Spain

In much of Spain, z is pronounced like the th in think, so:

• azúcar sounds like ah-THOO-kar

In Latin America, it is usually pronounced more like:

• ah-SOO-kar

It is basically a fixed expression meaning cotton candy.

So:

• algodón de azúcar = correct
• azúcar de algodón = not the normal expression

Even though the literal parts are understandable, the standard phrase is algodón de azúcar.

Yes, it sounds natural.

• Mi papá is very normal everyday Spanish
• compra is a standard present-tense verb form
• algodón de azúcar is the normal way to say cotton candy in Spain

So the sentence is perfectly fine for Spain:

• Mi papá compra algodón de azúcar.

Yes, that is grammatically correct.

The difference is mainly tone:

• mi papá = more familiar, warm, everyday
• mi padre = more formal or neutral

So both are correct, but mi papá sounds more like natural family speech.