flangeplumbingtoilet
The old PVC flange appeared to be sealed to the iron pipe by a rubber coating, which is not something I've encountered (in my limited research).
Will a simple push-tight toilet flange like this be good enough without additional welding? Its product page mention that it can be used inside cast iron pipes.
For cutting the pipe, go rent a chain pipe cutter (aka soil pipe cutter). It will make short work of the pipe and not be too messy. It will make a clean enough edge that a Fernco coupling (like you have a picture of) will work fine.
Obviously you will need to add some strapping to secure the horizontal run of iron pipe if you go this route because you don't want to put any extra strain on that rubber coupling.
I would not mess with trying to remove the flange. I think it will be easier to just cut the pipe.
Long Term Update: I did use one of these "expanding" repair flanges and it was fine. It's been over two years since the repair with no issues!
Toilet Flange OATEY Mfr #: 43539
Best Answer
See how the broken remnant of your old flange is marked "For Cast Iron"? The product you linked to in your question specifically says it's for PVC.
You should use a heavy duty product made for use with cast iron, and screw it securely to the floor with stainless steel screws after you set it. Something like this: