I am in the process of adding a second, 3 piece bathroom in my house. I am planning on running the drain through floor, parallel to the joists. I have enough room for proper slope. Here is my layout. Does this look suitable?
The vent for the lav comes off the top, not the bottom. You could use the lav to wet vent a shower if it were going though the roof, but as you have drawn it, anytime the shower runs by the lav stub up, it can pull. A vent is always from the top, not the bottom. Also if you were to wet vent the lav over the shower, it would need to be 2" in the wet portion.
Yes, though it would look better to me if you either just showed the trap arm for the lav without the vertical or if you included the p-trap into the drawing.