O terceiro está bem.

Because terceiro is functioning like a noun phrase: o terceiro = the third one / the third person / the third item, depending on context.

In Portuguese, ordinal numbers like primeiro, segundo, terceiro can be used this way with a definite article:

• o primeiro = the first one
• o segundo = the second one
• o terceiro = the third one

So o is not random—it marks it as the specific third one.

Because terceiro is the masculine singular form.

Ordinal numbers in Portuguese agree in gender and number with the noun they describe or replace:

• o terceiro = the third one/item/person (masculine)
• a terceira = the third one/item/person (feminine)

For example:

• O terceiro livro = the third book
• A terceira cadeira = the third chair

If the thing being referred to is feminine, you would say A terceira está bem.

Está bem commonly means is fine, is okay, or is well, depending on context.

In this sentence, it usually suggests that the third one/person is fine, okay, or acceptable.

A few possibilities:

• talking about a person: The third person is fine / doing well
• talking about an option: The third one is okay
• talking about an item: The third one is in good condition

So bem does not always mean only well in the health sense. It can also mean fine, okay, or satisfactory.

Portuguese often uses estar for states or conditions, while ser is more often used for identity, essence, or permanent characteristics.

Here, está bem describes a current state or condition:

• está bem = is fine / is okay / is doing well

Compare:

• Ele está bem. = He is well / He is fine.
• Ele é bom. = He is good.

So estar bem is about how something or someone is, not what it is.

Yes. Bem is very flexible in Portuguese. It can mean:

• well
• fine
• okay
• properly
• quite / very in some expressions

In está bem, it often sounds more like fine or okay than just well.

Examples:

• Estou bem. = I’m fine / I’m well.
• Tudo bem? = Everything okay?
• Fala bem português. = He/she speaks Portuguese well.

So learners should not think of bem as only a direct one-word equivalent of English well.

Usually, in standard Portuguese, no. You normally need the article here: O terceiro está bem.

Without the article, terceiro sounds incomplete in this sentence, unless it is part of a special context like a heading, list label, or very telegraphic speech.

Natural form:

• O terceiro está bem.

Less natural in normal speech:

• Terceiro está bem.

Portuguese uses definite articles more often than English in these kinds of noun phrases.

A careful approximation is:

oo tehr-SAY-roh es-TAH bayng

A few notes:

• terceiro has the stress on cei: ter-CEI-ro
• está has the stress on tá
• bem in Brazilian Portuguese ends with a nasal sound, not a fully pronounced English m

A more natural Brazilian pronunciation may sound closer to:

u tehr-SEY-ru is-TAH bẽy

Also, in connected speech, o often sounds like u.

It could be either. Portuguese allows this kind of phrase to be understood from context.

O terceiro can mean:

• the third person
• the third option
• the third item
• the third candidate
• the third one

Portuguese often leaves out the noun if it is already understood.

For example:

• Qual livro você quer? O terceiro. = Which book do you want? The third one.
• Como estão os alunos? O terceiro está bem. = How are the students? The third one is fine.

So context tells you what o terceiro refers to.

The plural would be Os terceiros estão bem if you mean the third ones are fine, though this is not very common unless there are multiple groups or sets.

Agreement changes like this:

• o terceiro está bem = masculine singular
• a terceira está bem = feminine singular
• os terceiros estão bem = masculine plural
• as terceiras estão bem = feminine plural

Notice that both the article and the adjective/ordinal change, and the verb also changes:

• está → singular
• estão → plural

Not exactly in the strongest sense. Está bem usually means is fine, is okay, or is doing well, rather than is good.

If you want The third one is good, Portuguese would more naturally use:

• O terceiro é bom. = The third one is good.

Compare:

• O terceiro está bem. = The third one is fine / okay.
• O terceiro é bom. = The third one is good.

So está bem often sounds more temporary, situational, or mild.

Yes. That is very common.

For people:

• Ele está bem. = He is fine.
• A terceira está bem. = The third one/person is fine.

For things:

• O computador está bem. = The computer is fine / okay.
• O terceiro está bem. = The third one is okay.

With things, it often means acceptable, working, or in good enough condition. With people, it often means fine in terms of health, mood, or overall state.

The normal word order is:

Article + ordinal/noun + verb + adverb

So:

• O terceiro = subject
• está = verb
• bem = complement/adverb

This is the most neutral and natural order:

• O terceiro está bem.

You could change the order for emphasis in some contexts, but the basic sentence learners should use is this one. Portuguese, like English, usually keeps this straightforward subject-verb-complement order in simple statements.