basement laundry project

I live in Walworth Wi and am embarking on a project in my basement to rearrange the wall that my laundry is on. When the ex and I moved in in 2002 there was a wooden cabinet similar to a kitchen cabinet on the wall with an enamel sink and space for the washer and dryer. A friend had listed old kitchen cabinets that he was getting rid of that I will be re-purposing for this project. I'm not as professional, but I am a very advanced home improvement level owner. The plan is to line the outer walls with 1" foam board and to cover those seams with tuck tape, then build a 4" wall on the wall with the 2 single pane wooden transom style windows. The iron water supply lines are being capped at the floor where they come up and replaced with PEX tubing from the ceiling. For the drains I am still trying to decide if I will leave them separated as they are now, or tie them both together with a loop incorporated to allow for vent. The problem with that portion is, I can't tie into the existing stack vent as it is on the other side of a poured concrete wall that separates the 2 sides of the basement. Will a 1 way check valve at a point above the top plate of the wall I build be sufficient? And, will I need to added 2x6 boxes that go from the concrete wall around the window frames and tie them into the wall, or how is best to frame those out, yet have good insulation and water barrier from the concrete? The arrangement is on the left as looking at everything is a 6' wall that is the poured concrete wall that I will be building a 2" deep wall for a place to run wires and to have wood to screw green board too. That will be perpendicular to a 15' wall that will be 2x4 construction with a treated sill plate. behind that wall will be the 1" foam board attached to the concrete wall. On the right I will be taking down part of the blue wood paneling and insulating with 1" foam board attached to the concrete exterior wall and I was thinking a 2" wall on that side too to save as much space as possible being it is a small space. Another problem with that corner is the water main comes in the right wall and runs approx 3' along the lower part of the wall and goes into the floor. It runs under the floor until it comes up on the other side of the wall that separates the 2 halves of the basement. I will be adding outlets along the way. Like 2 on the left, 2 on the back and maybe 1 on the right ways all connected to a GFCI outlet. Will I need to put the washer on it's own breaker? The dryer outlet will be replaced - it right now is that cloth tape out coating. I will be getting 10-3 to replace that and reuse the breaker it's on now. Thoughts on how to go about all this? I think I have the most of it all figured out.