Providing these emergency service things are fine there is the chance that the cord running to the disposal has developed a short or a wire has become disconnected. You will need to disassemble the unit to verify all wires remain securely fastened. The last conclusion is that the motor has burned out, in which case you will need to replace the disposal unit.
When you get to the house stand if front of the toilet and locate the water shut off valve. Should be down below the toilet on the wall. Just turn it off (righty-tighty) completely and flush the toilet. All the water should have left the tank, well at least most of it. If there is remaining water line repair get it out with paper towels or a rag. The important thing is that no more water came in. If it did then your valve is not shut all the way or not working and you need additional help.
If you need to add copper pipe make sure that you clean the old and new pipe by using sandpaper, inside and out. If it's not clean the solder will not flow into the joint. Another tip is to not over wrap the mail threaded pipe with tape, this can cause a leak. Twice around should be enough. Also, don't over tighten it.
These harsh working conditions would be hard for anyone. Plumbers need to make sure that they take all of the precautions they can take to remain uninjured, healthy and safe.
Be certain that the bathroom exhaust fan vents to the outdoors, not into the house or attic. If the exterior vent dampers don't operate properly or water line repair don't seat well have them fixed or replaced.
For a newly installed icemaker, you will need up to 24 hours to let the machine function and cool down. A newly installed icemaker may not work until the ice mold temperature has dropped to about 15F - 16F degrees. If you have just added a water line to the refrigerator, it may take up to about an hour and a half for the machine to start working. Also, a newly installed water line may have air in the line. It can sometimes take a few ice making cycles to clear the line of air.
Once you've located the water shut off, turn it off. Now, you can turn your attention to trying to contain the water damage caused by any leaking. Get towels, fans, blankets, or anything else to try and sop up water that is sitting on carpet or wood floors. Linoleum floors usually don't undergo much damage from having water sitting on them, unless there are cracks in the linoleum (often invisible) where the water can seep in. When your Queens plumber arrives, you will be one step ahead by following these instructions.