No!
Steel pipe.
Use PVC for the drain line. It does not require insulation.
A pipe cutter is the best tool to cut PVC pipe.
No.
Yes, if it is rigid PVC conduit approved for electrical installations. Don't use PVC water pipe as it will be rejected if inspected.
Most of the time it is 4 inch.
No, do not use glue. Use teflon tape or pipe dope on the threads. You should also make sure you always put the male PVC thread into the female metal thread. If you do it the other way you will tend to split the PVC fitting when you tighten the threads.
if your waste pipe is PVC and your glue is for PVC . yes! but make sure to use a primer(cleaner) on the pipe first.
Use teflon tape with a little pipe dope. If you don't ever have to take apart again then you can use glue which you are calling cement
Lead wipe a brass nipple into the lead pipe and then use a female adapter x PVC on the brass threads
Yes, for proper bonding of PVC pipe and fittings. Primer also code requirement.
PVC pipe is fine
NO..copper,black iron, galvanized for gas pipe.never use plasticp solvents or glue.gas does not react well with other chemicals.