Your real problem is that Massachusetts do not allow DIY plumbing. Briefly on your questions: No AAV for washers, washer must drain into an open standpipe that is trapped and vented. Your diagram indicates an unvented trap with a standpipe that is too short. It appears you have a vent available, but I'm pretty sure the connection the the main drain will have to be lower. Again, DIY is illegal in MA, you need to hire a plumber.