Hi guys. A small lesson in etymology: the verb "desculpar" comes from the word "culpa" which means guilt. If you want to say someone is guilty of something, you would say "culpado". In Portuguese "desculpar" actually means removing or undoing someone's guilt. So when you say "eu desculpo você" in Portuguese you're basically saying "I'm liberating you from your guilt", which is basically the same as forgiving.
The way of saying "I'm sorry" in Portuguese is the imperative "Desculpa", or the polite form "Peço desculpa". It looks the same as forgiving but this time you're asking for forgiveness, not "giving" it. "Peço desculpa" literally means "I ask for forgiveness" (or even more literally, "I ask you to remove my guilt"), while "Desculpa" means "Forgive me!" (but don't worry, you can say it at will in Portuguese, it doesn't sound so strong and harsh as in English).
No. "I apologize you." is not an English sentence. "I apologize to you." is, but it means "I ask you to forgive me." So it's not correct for this translation.
You could also say "I apologize for you." (more likely in the past or future tenses "( apologized for you" or "I will apologize for you.") This means something different too: "I ask someone else to forgive you."
Native English speaker here! "I apologise" is a gramarrically correct sentence, but carries a different meaning than "I forgive you." "I apologise" means you are sorry for something you did, and even then it's a little outdated. "I forgive you" means that someone else has done something wrong, and you forgive them for it. Hope this helps!
I believe it's regional. I am NOT an authority, let me be clear! I am just learning Brazilian Portuguese. However, I asked my husband's family this exact question, and they told me that it's a regional thing. My husband's family are all from the state of São Paulo, and they pronounce it with the soft 'd', as in the English 'j' sound in jeans.