Definition of a wet vent: a drain pipe that also serves as a vent pipe and extends from the most downstream wet-vented fixture connection to the most upstream fixture connection (the green item 4 in the below sketch).
Wet vents are typically used when plumbing a bathroom group. So yes the shower can also be vented by the wet vent along with the toilet. There is one major stipulation when wet venting multiple fixtures when a toilet is one of them: the toilet must be the last fixture connected to the wet vent. This means that in some situations you must use a symmetrical fitting (such as a double wye) in order to not break that rule. (Also, there can only be a max of two toilets connected to a wet vent).
Typical Bathroom Wet Vents:
The left sketch shows a typical arraignment when the toilet (WC) is located in-between the sink (LAV) and shower (SH). This arraignment relies on the use of a double wye fitting to avoid lines crossing while maintaining the toilet as the last fixture connected to the wet vent.
The right sketch shows how a bathroom wet vent might be arraigned without the use of the symmetrical fitting. There are many ways that a wet vent can be arranged, it all depends on the location of the fixtures and the direction the drain is coming from.
Components of a Typical Bathroom Wet Vent:
- Branch: Distance is unlimited but must be graded as per the diameter of the pipe.
- Trap Arm / Fixture Drain (shower): Distance is limited by the diameter of the pipe as the fall cannot exceed the pipe diameter. If 2" the distance would be 8' measured from the connection to the wet vent (where blue meets green).
- Fixture Drain (toilet): Distance is limited by the diameter of the pipe as the fall cannot exceed the pipe diameter. If 3" the distance would be 12' measured from the connection to the wet vent (where violet meets green).
- Wet Vent Branch: Distance is unlimited but must be graded as per the diameter of the pipe.
- Trap Arm (sink): Distance is limited by the diameter of the pipe as the fall cannot exceed the pipe diameter. Measured from the connection to the vent.
Issues With Your Sketch
The shower is connected to the toilet's fixture drain meaning that the the toilet is no longer the last fixture connected to the wet vent. (The issue with the toilet not being the last fixture is that the rush of water when the toilet is flushed could choke the vent connection of the other fixture (in your case the shower) and could result in siphoning out the fixture's trap.)
If you were to run the vent for the shower as shown in grey, the toilet would now be wet vented by the shower. The pipe downstream of the vent connection to the shower's fixture drain and the connection to the toilet would be the wet vent. The grey vent would be a dry vent, however the issue here would be that in most locations, you are not allowed to run the dry vent horizontal until you are 6" above the flood level of the fixture is serves and at minimum 42" above the floor.
The solution in your case would be to use a double wye fitting to symmetrical connect all three fixtures, similar to the left sketch.
I assume that the other fixture shown in the bottom left of your sketch in separately vented.
No. The portion from the wet vent connection (wye) to the 90 elbow under the toilet has a max distance determined by the grade of the pipe (3" pipe, 12' distance). The wet vent portion, from the vent connection at the sink to the wye that connects the toilet has no distance limit (it actually goes vertical). The portion from the vent connection to the sink is limited by the grade of the pipe (distance will vary as the pipe could be 2", 1-1/2", or 1-1/4" for a bathroom sink).