About the only thing you have right is the 4x3 "Y" in the main line. You cannot use a sanitary tee for the tub/shower. You cannot run the vents horizontal under the floor, and that "red" vent would have absolutely NO purpose or effect. How I, or any other plumber, would install the piping depends on a lot of factors none of which we know, such as where are the walls going to be located. If they could NOT connect a bathroom to the sewer line without running it above the floor, HOW could a floor drain be connected to it and work?