New bathroom tie-in for sewer line

[Mtnbikur]

I recently bought a house that was built in 1955. It used to be on septic. Not sure when, but all houses in the neighborhood were brought onto city sewer. Sewer scope for home inspection showed blue pvc/abs pipe after cast iron stack. Existing bathroom is at the back of the house and new bathroom location happened to be directly between original bathroom and street. I crawled under the house to locate a tie-in point close to where our new bathroom would be. I couldn’t find any sewer line at all in the area of the new bathroom. Next step, go to the stack and dig around the stack to see which direction the pipe heads. It heads towards the back yard. Which in hindsight makes sense with these houses being formerly septic.

My question(s).

1. Did the city dig a route that went around the house to the street?
2. Did they put the sewer line running thru everyone’s backyard with an eminent domain easement?
3. Is the a “U” within a couple of feet if I had kept digging?

And the question(s) that really, matter.

1. If you look at the attached picture, there’s a clean out. Can I throw a “Y” on that clean out with another clean out and my new waste line?
2. I’ve never worked with cast iron, so what sort of headaches are in my future tying into that clean out if it’s even possible?
3. Can I tie in with abs/pvc?

Thanks all