Basement Bathroom Venting

I purchased a home where the previous owner ran the plumbing for a basement bathroom. Installed is an ejector pit, two 2" pvc pipes, one 1 1/2" pvc pipe and one 3" toliet flange. My questions are 1) is this set up for a toliet, sink and shower and if so 2) how are these fixtures vented? I have included two pictures of how i think it should be vented (all based on where the sink drains into), and finally 3) can a 1 1/2" pipe be used for venting? Thanks.

are the pipes in the floor visible or do you think thats whats there?

The pvc pipes stick up out of the floor but the previous owner laid the cement so I can not tell what type of connections he used.

you only mentioned the 1 1/2 out of the floor, not an extra 2", but if I was a plumber (and I am) I would have run the wc right into the pit with 3" with a 3x2 wye going to the shower with a 2x 1 1/2 wye off that for the lav. That is the classic example of a wet vent. Your pic looks like option 1 is what you want. If you have an extra 2" just bring it above the lav height before you connect it to the lav vent. you need a check valve on the sewer line and in some states an alarm with a float to let you know the pump isnt working. I dont know illinois regs.

Thanks for the reply. The three pipes out of the floor, not including the wc, are two 2" and one 1 1/2". Knowing the need to vent, I wasn't sure if the 1 1/2" was the wet vent for the sink and the 2" shower or just the shower or for all three. If the 1 1/2" is fir sink and shower, then I assume the remaining 2" vent is for the wc ??

Looking into the pit, only one pipe (3"). discharged into it. Other than that, i have no idea what connections were used.

There will be a check valve on the sewer line.

Not sure I understand you one statement....If you have an extra 2" just bring it above the lav height before you connect it to the lav vent. Maybe you can elaborate on this.

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You need to check your local codes. Some codes just the pit needs to be vented