My home was built in the 50’s. I have a second floor 2 piece bathroom. The toilet is centred in one wall and I want to move it about 1 foot. A floor joist prevents me from doing this. I believe that I can reroute it slightly so that it runs below the joist into a closet ceiling and then into the bathroom floor. I intend to cut the cast iron pipe as marked and cut it again on the second floor. In red I marked the route. What should be the configuration of the sink drain and the toilet waste pipe connections?

 

I can't see if your waste stack continues upward as a vent. If it does continue upwards make sure you preserve that. And, make sure you strongly support the cast iron above before you cut out the pipe below. You don't want everything above sliding down.

It is good that you are planning on running below the joist and not cutting it as that's a major no no. Your really not changing much, just moving the connection point for the toilet down. Your new configuration probably will have the sink connection located above where the toilet ties in but it's all the same stuff connecting in a different order. If you look online there are a lot of pictures, diagrams and videos of what fittings you can use where.