If none of these materials is available to you you can always elect trustworthy plumber to soak rags or towels in hot water and wrap them around the frozen pipe. This will probably take longer than any of the methods previously mentioned.
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.
One other common design that is considered "washerless" was made famous by Delta and copied by several other makers. It uses little "cup" seals that fit over springs recessed in the back of the valve body. The springs press these "seals" against the cartridge and regulate the flow through little tapered openings in the cartridge. If you have one of these and it's dripping, changing these springs and seals will usually correct it. Here's a tip. Once you have the cartridge out of the way, insert a phillips screwdriver into the seal and pop both the seal and spring out. Stick the new ones on the end of the screwdriver to help guide them into place. This is especially helpful if you don't have long slender fingers.
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.
When the drain line stops up it is just a matter of calling an air conditioning contractor to come out and clear the drain line. While he is there he will add an algae preventative to the system to prevent future occurrences. Proper air conditioner maintenance is the key to preventing water line repair leaks.
If you plan to replace fixtures, you may be able to do this on your own. Buy the same style or functional fit and then turn off the water to make the switch. Follow the directions provided by the manufacturer to get the job done.
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.