If you set a battery on a concrete floor it will discharge.
This used to be true when batteries were made out of hard rubber or tar. Over time they would develop micro cracks making the case porous so putting them on a conductive surface could cause them to discharge. With modern plastics this is no longer true.
Fully discharging a battery will extend it’s life
Battery memory was true of NiCad batteries. NiMH batteries have much less of this effect and it is easily broken by running it through a full cycle. There are many types of batteries that can be damaged by running them down to zero.
Overcharging a battery can damage it
This is partially true. Most electronics can be damaged by excessive heat. Continuing to feed current through a battery after it is changed will heat it up and possibly crack the case or dry out the electrolyte. However there is a popular article being circulated warning about charging your cell phone over night. Many modern electronic devices have a charge controller in them that will reduce the current if the battery gets warm, and stop the charge current when the battery is full so that you don’t need to worry about it.
Brand X batteries last longer
In general an alkaline battery will last longer than a carbon battery, bigger batteries last longer than smaller ones, but there are actual tests for measuring battery capacity that don’t involve electric toy rabbits or flashlights. There are actually spec sheets on batteries that will give the capacity in milliamp/hours, abbreviated mAh. Unfortunately it is not easy to find the results of controlled tests without all the marketing.