Can this also be translated as "Every person needs to eat and to drink"
In my opinion, "needs to" sounds even better. Anyway, the second 'to' is not needed.
We actually haven't accepted repeated 'to' so far :D Added that possibility now.
Man was previously accepted for chlowiek, but here no. Is there a reason for this?
Yes, when referring to one specific person, człowiek can often mean man, but here it's different. Każdy człowiek refers to everyone, while every man only refers to males, at least in modern English, unless it's an idiom.
way not- each person has to eat and drink
Well, "each" rather refers to people of a certain group, but I think it should be okay...
Yes, that is accepted and it should have worked.