"Sou uma mulher negra."
In English, we have to determine the subject of the sentence, because there are subjects that have the same verb conjugation. As in Portuguese the conjugations are different, you know which is the subject only by conjugation of the verb, so no matter if they appear with or without a subject, the sentences have the same meaning. (if it has something wrong, I'm sorry, it's because I'm Brazilian, and I don't know writing English very well XD)
That is not true. At least in Rio and Sao Paulo (and in journalism), the politically correct way to say it is negro and negra. That is also what the media uses, and I have never seen the news use "preto" or "preta" to describe anyone, that would just be too awkward. They use "mulher negra" "homem negro" and "pele negra".
Isn't Negro is an English word for black people? I'm not a native English speaker thought, but when I read 'Uncle Tom's Cabin", the author used 'negro' to indicate the black people. Though it's from the time when enslaving was still legal, so the word might me a little offensive now. But regardless, shouldn't "I am a negro woman" be grammatically correct?
It's grammatically correct, but old-fashioned and possibly offensive.
There are a lot of different ways to refer to people of African ancestry in English. "Negro" at that time (1800s) was fairly polite, but would probably be considered slightly rude today. "Colored person" was the polite form for a long time, but sounds insulting now. "African-American" is what careful Americans, like politicians, say. "Black" is slightly less safe, but not rude. There's a six-letter word which sounds a little like "negro" in Uncle Tom's Cabin, which I won't type here because it's very offensive, although sometimes black rappers use it.
Incidentally, a small but possibly interesting point about the term "colored": it survives as part of the name of a major U.S. civil rights organization, the National Association for the Advancement of Colored People (NAACP -- "N-double A-C-P" orally), which was founded when the term was positive and still current (1909). They've stated that they don't think the term is offensive, even if it is outdated now, but that's a minefield I wouldn't walk through.
As for Arvore's six-letter word (and its five-letter slang variation), it is customary in English to say/write "the N-word" in most contexts where it must be brought up in order to avoid saying it -- navigating when it can be used as part of direct quotation or as part of an artistic endeavor is also a minefield, only now with nuclear mines. Best not to go there.
It all depends on in which country you are using these terms.
"People of color" in the US, includes all who are not caucasian or Asian, and we don't/can't use 'colored people' anymore. African Americans in the US have chosen to be called "Black", making 'Negro' offensive to them.
In Brasil, often people are called "Brown" which includes blends of ancestry along with Indigenous people. However, in Brasil, Negro, Nega, Negão are all used without offence amongst my friends, and as stated above, 'pele negra' or 'pele bem preto' (meaning that someone has beautifully black skin) are not unusual.
I hope the creators of this site can take these things into account- you don't want to mislead people, especially in what can be a sensitive subject (as it is here in the US).