How To Plumb & Vent My 3-Piece Basement Rough

The attached photos depict how the 3-piece bathroom rough-in located in our basement was installed by the builder.

The 2-inch PVC by the wall is assumed to be for the sink.
The 4-inch PVC (reduced to 3-inch) is assumed to be for the toilet.
The 2-inch PVC (with trap) is assumed to be for the shower (or tub).
The 4-inch PVC below the 3-piece rough is footer drainage.

I have also attached photos of what I believe is a 1 1/2-inch vent line that was extended into the basement from the first floor (by the builder as well) and am wondering if I am allowed to connect my basement bathroom vent(s) to this line.

As I have been read conflicting information online, can someone please tell me how all 3 of these pieces are plumbed and vented properly.

If there are further questions or additional information is needed, please ask.

Thank you in advance for the help!

Here, the toilet would not be vented as installed. In addition, they used a very circuitous way to install the piping.