O Pedro está muito motivado para estudar hoje.

In European Portuguese, it’s very common to use the definite article (o, a, os, as) before a person’s first name:

• O Pedro, a Maria, o João, a Ana, etc.

It doesn’t literally mean “the Pedro” in the way English would understand it; it’s more of a grammatical habit of the language, especially in Portugal and in informal speech.

So:

• O Pedro está muito motivado… = natural in European Portuguese.
• In English we have to drop the article: Pedro is very motivated…

Yes, you can.

Both are grammatically correct in European Portuguese:

• O Pedro está muito motivado para estudar hoje.
• Pedro está muito motivado para estudar hoje.

Differences:

• In Portugal, the version with the article is very common in everyday speech.
• In more formal writing, or in some styles, people may prefer to omit the article.

So you will hear and read both; using O Pedro is very normal and not “wrong” or childish.

• Estar is used for temporary, changing states or conditions.
• Ser is used for permanent characteristics, identity, or inherent qualities.

Está muito motivado suggests:

• Pedro is very motivated *right now / today (this may change).*

If you said:

• O Pedro é muito motivado.

That would mean:

• Pedro is, in general, a very motivated person (a permanent trait).

So in this sentence, está is correct because the motivation is about today (a temporary state).

Yes, está is:

• The 3rd person singular of estar in the present indicative:
  • eu estou
  • tu estás
  • ele/ela/você está
  • nós estamos
  • vocês/eles/elas estão

Functionally, here it corresponds to English “is” in “Pedro is very motivated…” and describes his current state.

Motivado is an adjective and must agree with the noun it refers to in:

• Gender (masculine/feminine)
• Number (singular/plural)

Here:

• Pedro is masculine and singular → the adjective must be masculine singular.
• So: motivado.

Other possibilities:

• A Maria está muito motivada. (feminine singular)
• Os alunos estão muito motivados. (masculine plural / mixed group)
• As alunas estão muito motivadas. (feminine plural)

Muito can be two different things:

1. Adverb = very, really

   • Does not change form.
   • Example:
     • muito motivado / muito motivada / muito motivados / muito motivadas

2. Adjective / pronoun = much, many, a lot of

   • Does change:
     • muito / muita / muitos / muitas
   • Example:
     • muita motivação (a lot of motivation)
     • muitos alunos (many students)

In muito motivado, muito is an adverb meaning “very”, so it stays muito for all genders and numbers:

• muito motivado
• muito motivada
• muito motivados
• muito motivadas

Here, para introduces a purpose / intention:

• …está muito motivado para estudar hoje.
• …is very motivated *to study today.*

In this context:

• para + infinitive = in order to [do something]

Other prepositions would change or break the meaning:

• a estudar → suggests being in the middle of studying (is studying), not purpose.
• em estudar → sounds strange here; em is not used for purpose with motivado.
• por estudar → in Portugal this would sound odd here; por doesn’t express purpose in this structure.

So para estudar is the natural, correct way to express motivated to study.

In European Portuguese, with motivado, the most natural and standard option is:

• motivado para [fazer algo]

Motivado a [infinitive] does appear, but:

• It is more common and more natural in Brazilian Portuguese.
• In Portugal, motivado para estudar sounds clearly better and more idiomatic.

So for Portuguese from Portugal, prefer:

• O Pedro está muito motivado para estudar hoje.

After expressions of purpose / intention with para, Portuguese normally uses the infinitive:

• para estudar = to study
• para trabalhar = to work
• para aprender = to learn

So:

• está motivado para estudar = is motivated to study.

Using a conjugated verb (estuda, estude, etc.) after para would either be incorrect here or would mean something different (e.g. part of another clause with a subject).

Yes, hoje can move, and Portuguese is quite flexible with adverb placement. All of these are grammatically correct:

• O Pedro está muito motivado para estudar hoje.
  → Neutral, very natural: motivated to study today.

• Hoje o Pedro está muito motivado para estudar.
  → Emphasises today in contrast with other days.

• O Pedro hoje está muito motivado para estudar.
  → Also possible; slightly more spoken and emphatic on hoje.

The most neutral and common version is probably the original:

• O Pedro está muito motivado para estudar hoje.

Yes.

• O Pedro está muito motivado para estudar hoje.
• Ele está muito motivado para estudar hoje.

Both are correct. Differences:

• O Pedro… names the person.
• Ele… refers back to someone who has already been mentioned in the conversation or text.

You wouldn’t normally say:

• O Pedro ele está muito motivado…
  (That sounds redundant in Portuguese, unlike some informal speech in other languages.)