I have an old house (100-years) and have a couple of questions about venting. Here's the details of each floor:

Basement - washer & utility sink, / shower, sink, & toilet
1st Floor - kitchen sink, garbage disposal, & dishwasher / sink & toilet
2nd Floor - tub, sink, & toilet

My main stack is 4-inch cast iron and appears to be in good/very good condition. Currently, I have a 1 1/2-inch PVC vent (I believe this to be a stacked vent) that runs from the basement to the second floor, where it becomes 2-inch cast iron, then runs to the attic where it ties into the main 4-inch stack that vents through the roof. I'm uncertain if it makes any difference, but each toilet on each floor is located within a few feet (approximately 3-6-feet) of the main stack. And, the 2nd floor bathroom sink vent ties into the system in the attic vs. on the second floor.

I currently have access to the vent pipe/stack on all three levels. My questions are:

#1 - Should I have a 2-inch vent vs. the current 1 1/2-inch?

#2 - Should I vent my basement bathroom group through an un-used 1 1/2-inch cast iron vent that exits the house on the basement stair landing, runs vertical along the brick exterior and vents above the roof/gutter?

#3 - Can I plumb my 1st floor bathroom sink drain into the current vent? In other words (if I have the language correct), can I wet vent my basement washer and utility sink?