Sei por que o filtro de óleo está sujo.

Because Portuguese often drops the subject pronoun when the verb form already makes the subject clear.

• sei = I know
• The ending -ei here clearly shows first person singular

So both are possible:

• Sei por que o filtro de óleo está sujo.
• Eu sei por que o filtro de óleo está sujo.

The version without eu is very natural and common.

Here, por que is used because it introduces an indirect question: why.

In this sentence, the speaker says they know why the filter is dirty:

• Sei por que o filtro de óleo está sujo.
• literally: I know for what reason the oil filter is dirty

This is different from porque, which usually means because.

A very useful quick guide:

• por que = why / for what reason
• porque = because
• por quê = why at the end of a clause or sentence
• o porquê = the reason

So in this sentence, por que is the standard written form.

In standard writing, the preferred form here is por que, because it is an indirect question after sei.

So the recommended version is:

• Sei por que o filtro de óleo está sujo.

That said, you may sometimes see porque in informal writing, but for learners, it is best to follow the standard rule and use por que here.

Because saber is used for knowing facts, information, answers, explanations, or how to do something.

Here the speaker knows the reason something is dirty, so saber is the correct verb:

• Sei por que... = I know why...

Conhecer is used more for being familiar with people, places, or things:

• Conheço o mecânico. = I know the mechanic.
• Conheço essa oficina. = I know that repair shop.

So:

• saber = know a fact / know why
• conhecer = know someone/something through familiarity

Because estar is used for a state or condition, while ser is used more for identity, permanent characteristics, or classification.

Here, dirty is treated as a condition of the filter:

• o filtro está sujo = the filter is dirty

That makes sense because a filter can be dirty now and clean later.

If you used é sujo, it would sound more like describing something as inherently dirty or characteristically dirty, which is not the normal idea here.

So in this sentence:

• está sujo = is dirty as a current condition

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

Here the noun is:

• o filtro = masculine singular

So the adjective must also be masculine singular:

• sujo

Examples:

• o filtro sujo = masculine singular
• a peça suja = feminine singular
• os filtros sujos = masculine plural
• as peças sujas = feminine plural

Since filtro is masculine, sujo is correct.

Because filtro de óleo is a normal noun phrase meaning oil filter.

Here, de óleo expresses the type or function of the filter:

• filtro de óleo = oil filter
• literally: filter of oil

Using do óleo would usually mean of the oil, referring to some specific oil, which is not the intended meaning here.

Compare:

• filtro de óleo = oil filter
• o filtro do óleo = the filter of the oil / the oil’s filter

In this sentence, the first meaning is what we want.

Portuguese often uses definite articles more regularly than English does.

• o filtro de óleo = the oil filter

The article o shows that we are talking about a specific filter, not just any filter in general.

Without the article, the sentence would sound less natural in normal usage here.

So:

• o = masculine singular the
• filtro = filter

Together:

• o filtro = the filter

No. In this sentence it is an indirect question.

A direct question would be:

• Por que o filtro de óleo está sujo?
• Why is the oil filter dirty?

But in your sentence, that question is embedded inside a larger statement:

• Sei por que o filtro de óleo está sujo.
• I know why the oil filter is dirty.

So the whole sentence is a statement, not a question, even though it contains the idea of why.

No. Normally, no comma is used here.

• Sei por que o filtro de óleo está sujo.

That is because por que o filtro de óleo está sujo is the object clause of sei. It is tightly connected to the verb, so no comma is needed.

Óleo means oil, and the accent mark shows where the stress goes.

It is pronounced roughly like:

• OH-lee-oh

The written accent in ó tells you the stress falls on that syllable:

• Ó-le-o

This word can be a little tricky because it has three syllables in careful pronunciation.

Here, sujo is an adjective describing o filtro de óleo.

The structure is:

• o filtro de óleo = subject
• está = verb
• sujo = predicate adjective

So sujo tells you the condition of the filter.

Yes, but the original order is the most neutral and natural:

• Sei por que o filtro de óleo está sujo.

You could sometimes hear other structures for emphasis, but they may sound more marked or literary. For learners, it is best to keep the standard order:

• Sei
  • por que...

That is the clearest and most natural version in everyday Brazilian Portuguese.