O dado está perto do peão.

Because Portuguese normally uses estar for location.

• O dado está perto do peão. = the die is near the pawn
• A chave está na mesa. = the key is on the table

Ser is usually for identity, classification, or more permanent characteristics:

• Ele é médico. = he is a doctor
• O dado é branco. = the die is white

So for physical position, está is the natural choice.

Here, dado means die, the singular form of the game object.

That can be confusing for English speakers because English uses die / dice, while Portuguese is regular:

• o dado = the die
• os dados = the dice

Also, dado can mean other things in different contexts, such as data or given, but in this sentence the game-related meaning is the one that fits.

Because perto normally takes the preposition de.

So the full structure is:

• perto de = near, close to

Then de + o contracts into do:

• perto de o peão → perto do peão

This kind of contraction is very common in Portuguese.

Do is a contraction of de + o.

• de = of, from, about, or part of a fixed expression depending on context
• o = the

So do literally comes from of the, but you should not translate it word-for-word here. In perto do peão, it simply helps form the expression near the pawn.

In this sentence, peão means pawn, the game piece.

That said, peão can also mean other things in other contexts, such as a laborer or ranch hand. Portuguese words often depend on context, and here the presence of dado makes the board-game meaning the most natural one.

Because they are grammatically masculine nouns, so they take the masculine singular article o.

• o dado
• o peão

Grammatical gender in Portuguese does not always match real-world sex or logic. It is simply a property of the noun, and the article must agree with it.

Yes.

Portuguese forms this pair regularly:

• dado = singular
• dados = plural

This is easier than English, where the traditional singular is die and the plural is dice.

They help show pronunciation.

• está: the acute accent shows that the stress falls on the last syllable: es-TÁ
• peão: ão is a nasal ending, and it is stressed

So peão is pronounced roughly like peh-OWN, but with a nasal sound at the end rather than a fully spoken n.

Yes. Próximo de and perto de can both mean near or close to.

• O dado está perto do peão.
• O dado está próximo do peão.

Both are correct. Perto de is very common and very natural in everyday Portuguese.

Yes, but O dado está perto do peão is the most neutral and natural order.

It follows a very common pattern:

• article + noun + verb + location expression

You might see a different order for emphasis, but for a learner, this version is the best one to use.