O prêmio está mais caro este mês.

Because estar is normally used for temporary states or conditions, while ser is used for more permanent characteristics.

So O prêmio está mais caro este mês suggests that the price is higher this month, implying a temporary or current situation.

• estar caro = to be expensive right now / at the moment
• ser caro = to be expensive in general

Since the sentence includes este mês, está is the natural choice.

Mais caro means more expensive.

This is the comparative form:

• caro = expensive
• mais caro = more expensive

Portuguese often forms comparisons with:

• mais + adjective

Examples:

• mais barato = cheaper / less expensive
• mais rápido = faster
• mais difícil = more difficult

Because caro agrees with o prêmio, which is a masculine singular noun.

In Portuguese, adjectives usually agree in gender and number with the noun they describe.

• o prêmio caro = the expensive prize/premium
• a taxa cara = the expensive fee
• os prêmios caros = the expensive prizes/premiums
• as taxas caras = the expensive fees

So here:

• prêmio = masculine singular
• therefore caro = masculine singular

Because the sentence does not explicitly say what it is being compared to.

In Portuguese, just like in English, you can say something is more expensive without stating the comparison.

So:

• está mais caro = it is more expensive

The listener understands that it is more expensive than before, than usual, or than last month, depending on context.

If you want to say than explicitly, Portuguese uses do que (or sometimes just que):

• Está mais caro do que no mês passado. = It is more expensive than last month.

O is the definite article, meaning the.

So:

• o prêmio = the prize / the premium

Portuguese uses definite articles more often than English does, and they are very common before nouns.

A quick comparison:

• um prêmio = a prize / a premium
• o prêmio = the prize / the premium

Este mês means this month.

• este = this
• mês = month

In standard grammar, este refers to something close to the speaker, including the present time, so este mês is a natural way to say this month.

In everyday Brazilian Portuguese, many speakers also use esse mês in the same kind of situation. So you may hear both:

• este mês
• esse mês

Both are common in Brazil, though este mês is perfectly correct and a bit more formal or careful.

This word order is very natural in Portuguese.

Structure:

• O prêmio = subject
• está = verb
• mais caro = description/comparative adjective
• este mês = time expression

So the sentence follows a common pattern:

Subject + estar + adjective/comparative + time expression

Examples:

• O aluguel está mais alto este ano.
• A gasolina está mais barata hoje.

You could move este mês for emphasis:

• Este mês, o prêmio está mais caro.

But the original order is very normal.

Prêmio most commonly means prize or award, but in some contexts it can also mean things like premium.

Since you said the meaning is already shown to the learner, the main grammar point is this: prêmio is a masculine noun, which is why the sentence uses:

• o prêmio
• mais caro

So even if the exact English translation depends on context, the grammar stays the same.

In Brazilian Portuguese, prêmio is pronounced approximately like PREM-yoo.

A rough guide:

• prê sounds somewhat like preh (but nasalized slightly in natural speech)
• mio / mio-like ending often comes out smoothly, almost like myoo or mee-oo, depending on accent

The stress is on the first syllable:

• PRÊ-mio

Also:

• ê is a closed e sound
• the r in prêmio is the soft tapped/flapped r because it comes after p

It is grammatically understandable, but it is less natural in this context.

Using é can sound like you are presenting more expensive as a more fixed characteristic, while está fits much better with a time-specific change like este mês.

So the best choice here is:

• O prêmio está mais caro este mês.

Yes, but the meaning changes.

Examples:

• este mês = this month
• nesse mês = in that month / in this month (depending on context, but usually referring back to something already mentioned)
• no mês passado = last month

So:

• O prêmio está mais caro este mês. = The prize/premium is more expensive this month.
• O prêmio estava mais caro no mês passado. = The prize/premium was more expensive last month.

Notice that when the time changes, the verb may also need to change:

• está for present
• estava for past

Mês is masculine:

• o mês

That matters because demonstratives must agree with the noun:

• este mês
• not esta mês

So:

• este = masculine singular
• mês = masculine singular

That is why the sentence says este mês.

Yes, that is possible if the context already makes it clear what you are talking about.

Portuguese often allows the subject to be omitted when it is understood from the situation.

So:

• O prêmio está mais caro este mês.
• Está mais caro este mês.

Both can work, but the full version is clearer, especially for learners or when introducing the topic for the first time.