In the sentence:"He leaves on a business trip for Japan". Shouldn't the writer have used the preposition "to"?
"I can't remember his name off the top of my head". What does "off" in this sentence mean?
'Leave/depart for' + destination is correct; they mean 'start going to'.
'Off the top of my head' means 'from my most accessible memory'. Analogous to 'I took the first newspaper off the top of the stack'.