Here's how I understand it. At least in the past, "Ah So" was a stereotypical phrase said by Japanese/Asian characters, at least in American movies. This probably went out of style by the 1970s or so. So, maybe it's okay that he uses stereo-typical language because he IS Japanese, and therefor is not making fun of Japanese, whereas if he were not Japanese (i.e. his name was McSweeney) the phrase might be making fun.

"Green" because he does gardening work. It is also the color of the Irish Shamrock. So it's a play on words.

I’m not familiar with this slang but perhaps because “green” could be a negative slang for an Irish person. To be green also means to be new, inexperienced at something but that would not be “racist”