Identifying Vent in Unfinished Basement & General Bathroom Layout

I am looking to finish my basement and wanted to get validation on my vent tie-in locations.

I believe I have correctly identified it in the photo (top right of photo).
I believe the builders have it routed directly to a drain.

• I plan on reducing the 3" to use for my dual vanity, should i just replace this 3"?

• I added a vent for the toilet, can i just use the one from the sink?

Also, would appreciate any helpful thought on the layout below.