What you have drawn is a typical wet vented bath group, as long as you are venting the lavatory and you don’t go over any maximum vent lengths, you do not need any additional vents for the toilet or the shower. Assuming you are using 3” for your branch off of your sewer to your toilet and 2” for the underground portion of the lavatory and shower, you can go as far as 10’ from the 3x2 wye to the toilet, then as far as you want to the lavatory, and as far as 8’ to the shower trap. After the 3x2 wye, the only pipe you can jump up above the plane of the wet vent system is the lavatory line. You cannot jump up the toilet or the shower lines as this will be “breaking” the vent for these fixtures. So the line you have shown going to the shower over the existing sewer cannot jump over the sewer, but it can go over the sewer — it must be graded from the shower trap to the 2” wye for the shower/lavatory without breaking the plane. Where you want to connect the kitchen line is perfect. Also, don’t be concerned with the “circle” of your shower drain. What you have drawn is exactly how it is supposed to be. Good job!
Different localities may have slightly different rules, but what I described is how it has been done in Virginia, just about forever.
Here is a link to a page that will give you a pretty good idea of what a wet vent is, with some pretty good drawings: https://www.reevesjournal.com/articl...-leap-of-faith