Rule 3m. states that "All batteries must be factory-sealed and voltage labeled by the manufacturer." Does this mean that (non-hazardous) home-made batteries like lemon batteries are not permitted?
Correct, any type of homemade batteries are not allowed per rule 3.m. A battery is defined as a device that utilizes a chemical reaction to generate voltage and current. Note that chemical reactions that result in a change in resistance are allowable in devices.