A pipe cutter is the best tool to cut PVC pipe.
Yes, if it is rigid PVC conduit approved for electrical installations. Don't use PVC water pipe as it will be rejected if inspected.
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.
Absolutely Not!
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
If you are screwing in -- yes -- If not -- you do not use pipe dope
I don't understand why you'd want to do that . CPVC glue is expensive, PVC glue is cheap and glues PVC pipe better.
PVC pipe is an acceptable product to use in chillers that contain glycol. You should never use galvinized pipe where glycol is used. Copper is acceptable as well.