I dont like exposed plastic water lines so I would want protection in any of variety of ways I thought of slipping insulation over hot and cold as well . But I dont think its required.
What about electrical are you allowed to leave a box like that with exposed romex? opr your running conduit?
I didnt get why the exposed stuff generaly I like it covered
Jeff: Your comments made me think. Everything in the photos from the two fire-break studs and up in first photo will be drywalled. I am going to set the dryer on a shelf I'm making from (2) 3/4" plywood pieces glued and screwed together. Since the shelf will have about a 5" gap between it and the wall, I revised the way it can be done.
First photo is new layout. Portion of drywall marked with X will be removed and access door installed. It will be 13" wide, and about 40" tall. Plenty of room to get at the hoses and get to dryer vent to clean it. Everything else there gets drywalled. Slanted board above fire breaks is actually roof of middle level of house, so will have to be well-insulated. I think washer box will be better suited to be hung lower, like in second photo, than in first photo. I will still have to run Pex pipes (well-insulated pipes, mind you) over the ceiling of laundry closet and down to washer box. Electrical boxes will be mounted as they are in first photo, all behind drywall. Washer box and pipes will be behind drywall doing it this way.
Third and fourth photos show roof vent and plumbing downward. A straight pipe will attach to pipe in fourth photo and run down to MagVent 90. If I could remove that upper 2 x 4 (I think it's a fire break) I'd be able to move vent back about 2". Not put it behind drywall, but move it back. I would still have a small space to insulate behind it. To run a pipe straight down from vent, though, I would have to cut out that section of top plate in third photo that people who built house mutilated almost to ruin. I'm not a structural engineer, but I don't think it would be a good idea to remove a section of load-bearing wall top plate.
Last photo shows the existing washer box. I never have liked this layout because it puts the washer hoses to the side of the washer where they can't be accessed. Besides that, I needed to raise it up and learned a lifelong lesson that you have to be extremely careful cutting Pex from a brass washer valve fitting to avoid grooving it with the blade so it leaks water no matter how many times you re-clamp it.