Very easy fix using bar solder with a composition of 40 -60 and acid free flux and the use of a wiping cloth that most older master plumbers still have
WeldBrazeTap and plugCut out and install a union
Would depend on the material the piping is made from
The best approach is using an alloy that contains more lead then tin as the melting point will be lower thus less chance of buring a hole through the lead pipe. Lead wiping is the best approach
If it is galv. pipe there could be a small hole on threads. You would have to replace pipe.
If the pipe is in good enough shape you can weld over the hole, BUT If there is one small hole rusted in the system it is a good sign the pipe is rotted. There will be many other holes soon. There are probably more holes than you know about. You will probably have to have an exhaust shop put in a new pipe for you.
solder it or cut it out and install new pipe. making sure when you cut you make cut where the pipe is still round and use fernco apts. to put back together. if it is in a tough place to do, best to get a plumber
Cut out the old piping and caulk a new cast iron bell and spigot with lead and oakum and test
They will not pay to fix the pipe, or will not pay for the clean up and damage to your property? They have to fix the pipe and clean up the mess caused by it. Any personal property, possibly not. That's why they sell renters insurance. You may be able to take them to small claims court to recover damages.
The exhaust pipe will need to be replaced, or, you can buy a quick-fix patch at your local auto parts store as a temporary fix. It's a treated "ribbon" about 2 or 3 inches wide that you can wrap around the exhaust pipe to cover the hole. The heat of the exhaust activates the chemicals in the "ribbon" to make it adherent. I believe the product is called a muffler repair kit.
Lead wipe a brass nipple into the lead pipe and then use a female adapter x PVC on the brass threads
Cut the pipe and remove it, fix pipe with a coupling.
Try some JB WELD or some good quality epoxy. Either will most likely work.