So, as I understand it, this bathroom exists as is, and was installed without vents for the shower and the sink. And according to your drawing, the vent is actually running up the inside of the bathroom. You don't show the actual piping runs, so I am assuming they run relatively straight from the P-traps to the stack. If they were shown on the original post, I don't remember them. And you don't indicate if the existing piping is readily accessible from below. But assuming you do have access to the shower drain piping, you may be able to vent the exiting line by installing a sanitee in the horizontal line at no less than a 45 degree off vertical and run the vent inside the existing wall that the door opens against. You could then tie into the existing stack in the attic, again assuming there is an attic above this bathroom.
If the existing piping does not allow the vent to be installed as described above, you should be able to revise the existing drain piping with a small jog so that it runs directly beneath that wall and then the vent piping can be installed up that wall as described above.
A similar modification could be performed for the sink drain venting, but with a different wall. Now if the walls around the pedestal sink are exterior walls with little or minimal access in the attic, you could use an AAV (Air Admittance Valve) in the wall. It would need to be installed in a box open to the bathroom. I dislike those, but that may be your best solution for the pedestal sink.
An AAV possibly could be used for the shower vent with the existing piping if there at least 4" above the P-trap to allow for proper installation. Again, I dislike those, but that could possibly be a solution for the shower vent with minimal work. Assuming there is a basement with adequately sized floor joist, see my sketch below.
If the existing piping does not allow the vent to be installed as described above, you should be able to revise the existing drain piping with a small jog so that it runs directly beneath that wall and then the vent piping can be installed up that wall as described above.
A similar modification could be performed for the sink drain venting, but with a different wall. Now if the walls around the pedestal sink are exterior walls with little or minimal access in the attic, you could use an AAV (Air Admittance Valve) in the wall. It would need to be installed in a box open to the bathroom. I dislike those, but that may be your best solution for the pedestal sink.
An AAV possibly could be used for the shower vent with the existing piping if there at least 4" above the P-trap to allow for proper installation. Again, I dislike those, but that could possibly be a solution for the shower vent with minimal work. Assuming there is a basement with adequately sized floor joist, see my sketch below.