Where do I connect the drain for my new sink in this layout and why is it better in that point specifically?
I would use a wye fitting on pipe # 3, run pipe coming off wye (45 degree angle) and use and 45 degree fitting to line up with center line of new sink,use a medium sweep to turn up  clean out tee and then 2x2x11/2 santee at proper height   Approximately 20” from floor of bathroom . Run vent up wall ,over and above finished ceiling and tie into new dry vent of same size or bigger