In containers designed to store them (not glass) and away from sources of ignition, and not accessible to small children (both are poisonous as well as flammable). Ideally, not stored inside the home.
The only time you should place kerosene in a heating system is if it is designed for kerosene.
When the petroleum industry started, the desired product was kerosene for home lighting lamps. Before the modern crude oil refinery was developed, oil was boiled and distilled in a single stage distillation similar to wiskey stills. Gasoline was the fraction that came off first and since the automobile had not yet been developed, there was no use for the gasoline. Gasoline was a waste product and was thrown out or burned to make more kerosene.
Kerosene should not be used as a home heating oil unless the unit is designed to do just that, kerosene may be used in a small amount to inhibit gelling of fuel oil during extremely cold weather.
None! Gasoline is refined petroleum, a hydrocarbon which is poisonous to drink or even breathe, which is why it pollutes the air when burned. (In the 19th Century gasoline and kerosene were used to kill body lice, but that's the only "therapeutic" use I can think of - don't try it at home!)
Keep the gasoline in a well-ventilated space away from your house. If you keep gasoline cans in your home, you run the risk of fires or exposure to fumes. Keep your containers in a shed or a specially-made flammable liquid storage cabinet outside your home.
Kerosene and home heating oil can be mixed in a oil furnace. Kerosene is thinner than heating oil. Mixed together will make the furnace burn cleaner.
Safely.
Typically cars either burn gasoline or diesel fuel if the engines are equipped to burn that. Kerosene is normally not used in a diesel but it will function in an emergency just as well as diesel fuel except that the injection parts will not receive much lubrication. But it will get you home in a pinch. If your question is can you use #2 diesel in a wick type kerosene heater then no. Diesel fuel will smoke and stink compared to kerosene. If your question is can you use #2 diesel in a kerosene heater that is like a salamander, then maybe. I use #2 diesel in my salamander and it works fine and heats my garage up ok. Kerosene does burn cleaner though.
Batteries should probably be kept in a drawer or probably in a small box.
There are home remedies involving Kerosene for treating arthritis. To find out more just type the words Kerosene and arthritis into your browser and you will get a selection of websites to look through for more info.
Odorless kerosene fuel can be found at most hardware stores, home improvement stores, or outdoor supply stores. Additionally, it can also be purchased online from various retailers. It is important to check the product specifications to ensure that it is indeed odorless kerosene.
One can purchase a kerosene heater in most building supplies and DIY stores. They can also be found online from Lowes, Home Depot, Amazon and eBay. Care should be taken to use them in well ventilated spaces only.