Eu olho para a árvore no jardim.

In Portuguese (including in Portugal), subject pronouns like eu are often optional, because the verb ending already shows the person.

• Eu olho para a árvore no jardim. = I look at the tree in the garden.
• Olho para a árvore no jardim. = Same meaning; the subject is understood as I from the form olho.

You usually include eu when:

• You want to emphasize the subject:
  
  • Eu olho para a árvore, mas tu olhas para o carro.
    I look at the tree, but you look at the car.
• You need to avoid ambiguity in a longer context.

So yes, Olho para a árvore no jardim is perfectly correct and very natural.

Yes, there are two different words spelled the same way:

1. olho (from the verb olhar)

   • Verb form: 1st person singular, present tense: eu olho = I look.
   • Infinitive: olhar (to look).

2. olho (noun)

   • Means eye.
   • Example: o olho = the eye; os olhos = the eyes.

In your sentence:

• Eu olho para a árvore no jardim.
  olho = the verb form of olhar (I look), not the noun eye.

With the verb olhar (to look), Portuguese normally uses the preposition para to mean look at:

• olhar para alguém = to look at someone
• olhar para alguma coisa = to look at something

So:

• olhar para a árvore = to look at the tree

olhar a does exist but is:

• More formal / literary, and
• Much less common in everyday European Portuguese.

In everyday speech from Portugal, olhar para is your default for look at:

• Eu olho para a janela. = I look at the window.
• Eles olham para o céu. = They look at the sky.

Yes, you can use vejo, but it changes the meaning slightly:

• olhar (para) = to look (at) – you are directing your eyes intentionally.
  
  • Eu olho para a árvore. = I look at the tree.
• ver = to see – you perceive something visually, not necessarily on purpose.
  
  • Eu vejo a árvore. = I see the tree.

So:

• Eu olho para a árvore no jardim.
  I deliberately direct my gaze at the tree in the garden.

• Eu vejo a árvore no jardim.
  I see the tree in the garden (it is within my field of vision).

Both are correct, but they are not identical in meaning.

In Portuguese, countable nouns almost always take a definite or indefinite article, unless there is a special reason not to.

Here:

• a árvore = the tree (definite article, feminine singular)

You normally need that article:

• Eu olho para a árvore. ✅
• Eu olho para árvore. ❌ (sounds wrong or very foreign)

Other examples:

• Vejo o carro. = I see the car.
• Compramos uma casa. = We buy a house.

So a is just the regular definite article that goes with árvore.

árvore is feminine in Portuguese, so it takes the feminine article a:

• a árvore = the tree
• as árvores = the trees

There is no strict rule that tells you the gender just from the ending in this case; it is mostly memorized.

Some hints:

• Many words ending in -e can be either masculine or feminine:
  • o nome (the name) – masculine
  • a ponte (the bridge) – feminine
  • a árvore (the tree) – feminine

When you learn a noun, it helps to learn it together with its article:

• a árvore, o carro, a mesa, o jardim.

no is a contraction of the preposition em (in/on/at) + the masculine singular article o (the):

• em + o = no

So:

• no jardim = em o jardim = in the garden

But em o is almost never written; the normal written and spoken form is the contraction no.

Other related contractions:

• em + a = na → na escola (in the school)
• em + os = nos → nos jardins (in the gardens)
• em + as = nas → nas árvores (on the trees / in the trees, depending on context)

Each preposition gives a different idea:

• no jardim = in the garden (location; from em + o)

  • Eu olho para a árvore no jardim.
    I look at the tree in the garden.

• para o jardim = to the garden (movement or direction)

  • Vou para o jardim. = I go to the garden.

• ao jardim = to the garden, usually as an indirect object or direction (from a + o)

  • Vou ao jardim. = I go to the garden.
    (In Portugal, ir ao is very common for going to a place.)

In your sentence you are not moving to the garden, you are just saying where the tree is, so you use em → no jardim.

Yes, you can. In European Portuguese:

• Eu olho para a árvore no jardim.
  Present simple. Can mean:

  • a habitual action: I (often) look at the tree in the garden.
  • a current action, depending on context: I am (now) looking at the tree in the garden.

• Eu estou a olhar para a árvore no jardim.
  Present progressive (very common in Portugal).

  • Focuses on what is happening right now: I am looking at the tree in the garden (at this moment).

Both are grammatical. The second one makes the idea of a current ongoing action clearer.

Approximate pronunciation (Portugal), using English-like hints:

• Eu → like “ehw” or “eu”, a bit like English “eh” + “oo” compressed [ew].
• olho → “O-lyu”
  
  • lh is a single sound, like the “lli” in English “million”.
  • Stress is on o: Ó-lho.
• para → in Portugal often sounds closer to “pɐ-rɐ”, something like “puh-ruh”, both vowels reduced.
• a → often very short, almost like “ɐ”, a quick neutral sound.
• árvore → “AR-vu-rë”
  
  • Stress on ÁR.
  • Final -e is usually a light “ë” sound, not fully like English “ee”.
• no → close to English “no”, but shorter.
• jardim → roughly “zhar-DIH~”
  
  • j = like the s in “measure”.
  • Stress on -dim.
  • Final m nasalizes the vowel: -im is nasal, like French “vin” but with i.

Spoken quickly, it tends to link together:

• Eu olho para a árvore no jardim.
  → something like: “Ew Ó-lyu pɐrɐ AR-vu-rë nu zhar-DIH~”.

The acute accent in árvore has two main functions:

1. It shows where the stress is:

   • ÁR-vo-re: the stress falls on the first syllable ÁR.

2. It indicates the quality of the vowel:

   • á is an open [a] sound (like in English “father”, depending on accent).

Without the accent, arvore would:

• Be read with the stress on the second syllable by default (ar-VÓ-re, which is wrong), and
• Not follow standard spelling rules.

So the accent tells you both where to put the stress and how to pronounce that vowel.

You need the plural for trees:

• a árvore → as árvores (the tree → the trees)

The full sentence:

• Eu olho para as árvores no jardim.
  I look at the trees in the garden.

Changes:

• Article a (feminine singular) → as (feminine plural)
• Noun árvore → árvores

Everything else stays the same.

Eu olho no jardim para a árvore is unusual and mainly sounds like:

• I look in the garden for the tree (or I look in the garden, towards the tree), depending on intonation.

The normal and clear way to say I look at the tree in the garden is:

• Eu olho para a árvore no jardim.

Word order in Portuguese is relatively flexible, but:

• Prepositions tend to keep their normal combinations:
  • olhar para algo (look at something)
  • em algum lugar / no jardim (in some place / in the garden)

When you shuffle them too much, the meaning either changes or becomes unnatural.