I would say "when I arrive home". "At home" generally means "in your home" and is used to indicate a place where you are located rather than a destination. Example: I was at home last night. When will you be at home? I left my wallet at home. On the other hand, we often say "to arrive at" a destination. Ex: When did he arrive at the airport? So I think you could say either "arrive home" or "arrive at home".

Both are okay to use but "I arrive home" is better because it's shorter, and we like to write and say things shorter in English. :-)

Both are fine, but a little formal. I think that in America most people would say "When I GET home . . . "

i think i arrive home is correct