It is correct to say: "He has gone home." You need a subject ('He' or some other singular noun : 'John', 'The girl', 'No one', ...)
To say "you went home" in French, you would say "tu es rentré(e) chez toi."
If we mean "he returned to his house" we say "He went home." But in other possible usages 'went for home' might be correct, using the informal verb "to go for," meaning to like a lot, to choose or to make an attempt at. For example, "Having to choose between home and office, he went for (= chose) home" and "Thinking that Papi's line drive had gotten past the shortstop, Youk went for home." You could also say, "He left for home" or "He headed for home." In this case "for" means "in the direction of". It's also correct to say something like "He went for a change of clothes" or "He went for eggs and bread."
okay and then what?
Just like that. You say, "Is she okay?"
we say d'accord or okay.
In Yiddish, you can say "eynzik" to mean okay.
In Canada it is okay to have your twelve year old at home alone, no younger than that.
I would say that it is okay for you to say that... but i would not brag about it..
"I just do okay".
In Punjabi, you can say "theek hai" to mean okay.
...went home to me.