**** no, it's not safe! And I can list numerous reasons why.
• It will produce Carbon Monoxide
• by leaving the door open, it will ruin the oven's thermostat that indicates when the oven has reached the specified temp therefore making the oven useless in the future.
• by leaving the door open, it can also cause the oven to overheat due to the above statement and go kaboom
• the oven will also burn off the oxygen inside your home making it difficult to breath eventually, unless you are also using your heater which takes air from the outside and brings it in.
• depending on the kind of appliance you have, there might be a flame in the back which is the source of the heat. If that flame went out and you weren't aware of it, your stove will continue to emit flammable gas. And all it takes is one itty bitty spark of static electricity to ignite that gas and destroy your home.
• last but not least. This isn't safety related though. Your electric or gas bill will sky rocket through the god damn roof. Is paying an additional $1000 a month worth risking all of the above and your life?
Jesus christ! I just noticed the part about the water! That's even more ******* stupid! That water will evaporate, condense inside the oven and guarantee to destroy the entire appliance and make it explode! Please take my advice and either convince your mom to not use the oven as a source of heat or go to/call up your local police station and tell them your mom is putting everyone's lives at stake.