han gick...he walked
han åkte...he travelled
Am I correct?
Yes and no. Åka means to "engage in transport by a vehicle but not propelling or steering it". In an expanded sense, it's often used to mean travel too, such as in the sentence "vi åkte till Spanien" (we went to Spain).
När åkte han hem? Isn't like "When he went home?
"Went" is the past of "to go", and since it's a question the correct would be "When did he go home?"
It is the past, so correct is "went" not "go". There are many logical misunderstandings and mistakes.
varför inte "hemma"?
Is not "drive" an appropriate translation, too?
I guess that's "kör" or "körde".