Hey! I have a question. Umm I understand if you're saying Eu conheço o menino that you use conheço and not sei. Is that because sei has to do with like something you're aware of because you already know it. Like ex: Eu sei matemática. But I want to know about if you are referring to someone else. Ela conheçe o menino or ela sabe o menino. Also ex: if someone says, you make me happy, how would I respond? Eu sei? Or can I say eu conheço?
For actions (i.e. verbs), always use saber.
My son doesn't know how to speak yet = Meu filho ainda não sabe falar
But we can say eu sei Matemática or eu sei francês or eu sei essa questão, because the verb is implied: eu sei (fazer/praticar) Matemática ; eu sei (falar) francês ; eu sei (fazer) essa questão
How about, "I know of the boy" or, "I know about the boy"?
Just one for instance: a housemate confronts another saying, "I know about your boyfriend; you do not need to keep hiding him." In this case the housemate knows there is a boyfriend, but maybe does not know him (or even his name), only that he exists on a physical level.
"Do you know who is coming today? Yes, I know about him but I do not actually know him [because we have not met yet]."
"Do you know the boy? Not personally, but I know who you are talking about. He's very popular at school."
Correct, only people and objects have genders. In this case you have two different verbs in Portuguese that translate to the same word in English, but with different contexts.
It's like how in English the word "run" can mean different things: you run an engine, you run a race, you run water through the tap/faucet.
There are similar words in Portuguese and other languages, which means you need to check for context in the sentence, not just direct literal meaning in the individual words — which is a really common mistake when people learn another language. :-)