u/Airado

The 2 copper line (painted white) and PVC drain line is installed by him.

My main concern is the PVC drain since it is an exterior wall, from the right, the first 2 studs are under a window, 3rd stud is a king stud for that window, forth is a normal exterior stud. Stud is 3 inches by 2 (old house). Drain line is 1.5 inch internal.

The copper supply line looks concerning but is less problematic since these are partition walls. I plan on adding shoes and nail plates.

But I have a bigger project that involves adding a supply line and drain pipe through 3 2x8 floor joist. The plumber recommended copper supply line for that project. Should I hire him again?

2x8 is already weak enough so I'd be concerned if he start notching too much.

The previous owner converted every trap in the house into S traps for some reasons.

In order to not open walls, my plumber fixed my kitchen S trap by connecting it to a wet vent in the basement, after the vertical drop. This new connection is circled in red.

I am having trouble visualizing how this helps with the siphoning effect. I thought the vent has to be connect on top of the p trap (where the text "S-trap" is).

Is this design fine, or will this not solve anything?

forgot to mention this replaced an AAV where the text s-trap is. it is below the sink and leveled with the disposal