Legally I don't think you're supposed to as it will contaminate the soil. I know there's a legal term for it but I can't think of it at the moment. However, who ever knows what to do with your leftover cooking oil.
Most definitely Not. There are recycling centers that will take used batteries and oil because they are very toxic. These are not items I would want lying around in my backyard. You can check around your city to find a recycling center hopefully near you. Your local county government may have helpful information on how to properly dispose of these toxic items.
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