New Bathroom Sewage Ejector Pump/ Pit Tie In

I am adding a bathroom in my basement. After much research I decided to go the sewage ejector pump/pit route. I have a 90 year old bungalow with a 4" cast iron soil stack and 2" galvanized vent. The main floor bath is directly above the new bathroom location. When we bought the house, there was a toilet only in the basement. After breaking the concrete around the stack and digging around I found the 4" cast iron transitioning to 6" clay (via a 4" sanitary tee w/ a 2" side inlet) and then out to the city sewer. I didn't like possibly damaging the clay so I went with the pump/pit option. I have the DWV system designed & dry fitted which brings me to my questions (I will post pics when I get a chance) :

1) I have cut off the original closet flange to make room for the new toilet location. Is a fernco cap suitable for under slab application?

2) I was thinking of cutting a no-hub 4" c.i. wye and then tying the sewage discharge into that. Since I have to cut into the 2" galvanized vent to tie in my new vents anyway, can I use the remaining stub coming up from the original sanitary tee w/ side inlet as my tie in from the pump?

3) I read that the pump/pit should be vented separate from the rest of the venting, however this isn't really feasible. Why is it not ok to tie into the same vent? Can I vent out the side of the house?

Not everything is clear to me without seeing exactly what you have to work with. A sewage ejector discharge is normally 2". You will need to cut a C.I. 4x4x2 wye into the existing building drain to connect the pump discharge. I prefer to plumb the discharge from the basin up to the ceiling and then back down to the drain connection. Though it is not required, it is good to have pitch in any horizontal section of the discharge, as this allows the piping to gravity drain and self-scour.

You can't have dead-ended piping in your drainage system. Instead of capping the existing closet flange, you should do what is needed to remove the unused piping or at least remove the point of connection to the rest of the system.

A common size single bath basin requires a 2" vent. The plumbing for a bath group requires a 2" vent. You need another vent. This vent will have sewer gas coming out of it. No plumbing code allows a vent to discharge out the side of a house. Installing a new vent might not seem feasible to you, but it can be done.