Does the Plywood Around the Toilet Flange Need to be Replaced

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.

Yep, you've got to cut it and should then use a Fernco coupling to plumb a modern PVC flange into the system. In the past I've tried unscrewing cast iron but it always breaks, sometimes shattering past a convenient cut point!