Duracell FTW
To be honest no, Energizer batteries are not more cost effecting in the long run. Battery technology is a very competitive area and none of the major companies (energizer, Duracell, etc.) has a major lead over the others. Even the "generic" brands are quite good, so I would suggest going for the lowest price rechargeable battery.
How long a battery lasts actually depends on what type of appliance it is used with. In flashlights, Energizer often lasts the longest in tests. Duracell is good for many things, although personal booklights seem to drain Duracell very quickly. It works well for lanterns and the like though. EverReady is generally a little below Duracell and Energizer. Rayovac is another brand that might be tried.
There are several long lasting and dependable 9v batteries available. Duracell Coppertops are a good choice as well as Ray-O-Vac and Energizer Industrial.
Battery brand isn't that important. The time to charge is mainly dependent on the capacity of the battery and the capacity of the charger. Any reasonable modern charger should sense when the battery is full and cut power when it's done. It can take some hours for a full charge.
About eight hours
it take an duracell battery in a flashlight non-stop lasts exactly 15 hours
energizer the long lasting stuff
Energizer batteries are just like any other battery except more expensive.
This depends on the working conditions.
there is no correct answer
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Whether it says it will or not, battery chargers will charge any battery, as long as they are for the same voltage. The charger puts out a set voltage, it doesn't know whether the battery is Energizer or not.