Eu não sei a razão.

Yes. In European Portuguese you usually drop the subject pronoun when it’s clear from the verb form.

• Eu não sei a razão = Não sei a razão
• Both mean I don’t know the reason.
• Eu is only needed for emphasis or contrast, e.g. Eu não sei a razão, mas ela sabe (I don’t know the reason, but she does).

In Portuguese, não almost always comes directly before the conjugated verb.

• Correct: Eu não sei a razão.
• Incorrect: Eu sei não a razão.

For compound tenses with an auxiliary, não goes before the auxiliary:

• Eu não tenho sabido a razão. (very rare sentence, but structure is: não
  • tenho
    • sabido)

Portuguese uses definite articles (o, a, os, as) more often than English.

• a razão = the reason (a specific, known reason)
• Bare razão (without an article) is possible but rarer here, and sounds more abstract or formulaic.

In this sentence, the speaker is clearly talking about a particular reason, so a razão sounds natural and idiomatic.

Yes, razão is a feminine noun, so it takes the feminine article a.

• a razão (the reason)
• uma razão (a reason)

If you look it up in a dictionary, it will appear as something like razão (f.), meaning feminine noun. There is no o razão.

Sei is the 1st person singular (eu) present tense form of the verb saber (to know – facts, information).

Saber is irregular in the present tense:

• eu sei – I know
• tu sabes – you know (informal singular)
• ele / ela / você sabe – he / she / you (formal) know
• nós sabemos – we know
• vocês sabem – you (plural) know
• eles / elas sabem – they know

So you must memorize eu sei, not eu sabo.

Saber and conhecer both translate as to know, but they’re used differently:

• saber – knowing facts, information, how to do something
  
  • Eu não sei a razão. – I don’t know the reason.
  • Eu sei a resposta. – I know the answer.
• conhecer – being familiar with people, places, works, etc.
  
  • Eu conheço a Maria. – I know Maria.
  • Eu conheço Lisboa. – I know Lisbon / I’m familiar with Lisbon.

So Eu não conheço a razão sounds wrong; you need saber for this sentence.

Yes, some natural alternatives are:

• Não sei porquê. – I don’t know why.
• Não sei o motivo. – I don’t know the reason/motive.
• Não faço ideia. – I have no idea. (more informal)
• Não sei por que é que isso aconteceu. – I don’t know why that happened.

But Eu não sei a razão is clear and correct, just a bit more formal/literal.

Approximate European Portuguese pronunciation (simplified):

• Eu – like “eh-oo”, often almost like “eu” in “euro”
• não – roughly “naung”, with a nasal vowel (like French “non” but with an a colour)
• sei – like English “say”
• a – like “uh” (a very short a)
• razão – roughly “ha-ZAUNG”:
  • initial r is a throaty sound (like French or German r)
  • z like English z
  • ão is a nasal sound, close to “aung” in “sung”, but with the lips more rounded

Spoken at natural speed, it links quite a bit: Eu não sei a razão.

No, those orders are ungrammatical.

• Standard order: Eu não sei a razão.
  • subject (Eu) – negation (não) – verb (sei) – object (a razão)

If you replace a razão with a pronoun, you might see:

• Eu não a sei. – I don’t know it.

But you don’t say Eu sei não a razão or Eu não sei razão in this context.

You mainly use the past tenses of saber:

• Eu não sabia a razão. – I didn’t know the reason / I didn’t use to know the reason.
  
  • Imperfect tense (sabia): ongoing or background in the past.
• Eu não soube a razão. – I didn’t find out the reason / I never got to know the reason.
  
  • Simple past (soube): a completed event (learning or not learning at a specific moment).

So you choose between não sabia and não soube depending on the nuance you want.