Este café está mais quente do que o outro.

Este means this and traditionally refers to something close to the speaker.

• este café = this coffee
• esse café = that coffee / this coffee near the listener
• aquele café = that coffee over there

In Brazilian Portuguese, everyday speech often uses esse where textbooks might expect este, so Esse café está mais quente... is also very common in conversation.
Still, este is completely correct and sounds a bit more careful or formal.

Portuguese usually uses estar for a temporary condition or state, and ser for a more permanent or defining characteristic.

Here, the coffee being hot is a temporary state, so:

• O café está quente. = The coffee is hot.

Using é quente would sound like you are describing coffee in general as something that is hot, not this specific coffee right now.

This is the basic comparative pattern for more ... than:

• mais = more
• adjective = description word
• do que = than

So the structure is:

[thing] + está + mais + [adjective] + do que + [other thing]

Example from the sentence:

• Este café está mais quente do que o outro.
• literally: This coffee is more hot than the other.
• natural English: This coffee is hotter than the other one.

Yes. In Brazilian Portuguese, both are used.

• mais quente do que o outro
• mais quente que o outro

Both mean the same thing here.
Do que can sound a little clearer or slightly more formal, while que is very common in everyday speech.

Unlike English, Portuguese usually does not create a separate comparative form for most adjectives.

English:

• hot → hotter
• cold → colder

Portuguese:

• quente → mais quente
• frio → mais frio

So instead of changing the adjective itself, Portuguese normally adds mais before it.

Here o outro means the other one.

Since outro is standing alone and replacing the noun café, Portuguese normally uses the article:

• o outro = the other one / the other coffee

If the noun is stated explicitly, you can say:

• o outro café
• sometimes also outro café, depending on the context

But in this sentence, o outro is the most natural way to mean the other one.

It matches in number, but not visibly in gender.

• masculine singular: café quente
• feminine singular: sopa quente
• masculine plural: cafés quentes
• feminine plural: sopas quentes

So quente is one of those adjectives that has the same singular form for masculine and feminine, but it still adds -s in the plural.

Yes, that is grammatically correct, but it is less natural if the context already makes it clear that both things are coffees.

Portuguese, like English, often avoids repeating the noun:

• ...do que o outro = ...than the other one

That is why the original sentence sounds smoother and more natural.

The accents show stress and are part of the correct spelling.

• café: the stress is on the last syllable → ca-FÉ
• está: the stress is on the last syllable → es-TÁ

These accents are not optional. They help show how the word is pronounced and sometimes distinguish words from other forms.

A rough pronunciation guide is:

ehs-TEE kah-FEH es-TAH maiz KEN-chee doo KAY oo OH-troh

A few notes:

• café sounds like kah-FEH
• está sounds like es-TAH
• quente is roughly KEN-chee, though the first vowel is actually nasalized in real Brazilian pronunciation
• do que often sounds like doo KAY
• o outro may run together a bit in natural speech

A more IPA-style version is roughly:

/ˈes.tʃi kaˈfɛ esˈta majz ˈkẽ.tʃi du ki u ˈow.tɾu/

Pronunciation varies a bit by region, but this is a good Brazilian reference point.