Hi again,
The crank light is self contained in that you dont have to hook anything up or do anything else like that. The crank is right on the flashlight so there is nothing to connect. If you wanted to take it apart and use the crank to charge other batteries you'd have to do some experimenting to see how well it would work with other batteries and of course it would have to be connected correctly to get it to work. You might also need a regulator circuit or charger circuit.
If you are in the sun all day you might get some benefit from solar panels. Since it's hard to judge from here i might suggest that you get a smaller lower cost panel and use that as a test to see how well this works out in practice with your typical routine and locations. You can then scale up later. As you said, maybe a small one to charge your cell phone would be a good place to start. You can then do some calculations to see what you would end up needing to charge more batteries for say your fans or other things. More about that in a minute.
You are asking the right questions that's for sure, and one of them about the batteries is also a good one. The lead acid batteries are not as efficient as most other types, and are used mainly to get a large amount of storage for a lower cost. Another two types are NiMH and Li-ion. Li-ion are the best but they require more care in charging. A special charger has to be used to match the battery size and capacity to some degree. NiMH are easier to use but you do have to string them in series to get some usable voltage beacuse they are only 1.4v each. Li-ion have terminal voltage around 4v or a little less. I would suggest that you read up on Li-ion and NiMH a little before you decide. A special kind of NiMH called "low self discharge" are better than the run of the mill NiMH cells.
Now back to the calculations...
You can get by with some simple calculations with batteries because they work mostly on current (amperes or amps). The terminal voltage is also important of course, but you simply match the battery voltage up to the application. If you have a fan that runs on 12v then you need batteries that put out 12v or close to that. The current is what is important for calculating the charging and discharging needs which affects the run time of the equipment.
As i said, it's very simple and only requires multiplication and division. If you charge a battery for 1 hour with 1 amp, you have 1 times 1 equals 1 ampere hour of charge in the battery (we'll talk about battery efficiency in a minute). If you charge a battery with 2 amps for 1 hour, that's 1 times 2 equals 2 ampere hours of charge. Charge for 3 amps for 10 hours and that's simply 3 times 10 or 30 ampere hours. Ampere hours is often written as "Ahr" or "AHr" or similar for short. Thus 30 ampere hours is written 30AHr for example.
Now say we did charge a battery at 3 amps for 10 hours and so we now have 30AHr in that battery, and we want to run a fan that requires 3 amps. The number of hours run time we get is approximately 30 divided by 3 or 10 hours. In other words, we divide the AHr by the current in amps. If we had only charged that battery with 9AHr we would have only gotten 9/3=3 hours run time. So you start to see how simple this is.
Now battery efficiency also comes into play though which makes it a little more complicated, but not too much. The amount we charge the battery is not exactly what we get out of it because there is a charge efficiency associated with each battery type. For example, using a lead acid battery we would have to put in about 1.4 times more charge into it than we would get out of it. Thus, if we have a fan that runs on 1 amp and we want to run it for 10 hours then we have to charge that battery for 14 hours at 1 amp. So you see we charged for 14 hours but only got out 10 hours of run time. In other words, the more exact run time comes from dividing by the current of the device and also divided by the charge efficiency (really called "charge acceptance") of the battery. We charged for 14 hours at 1 amp so that's 14 AHr, then we divide that 14 by 1 (the current of the fan) and divide by 1.4 (the efficiency) and we get 10, which is the run time in hours.
Now there's the battery capacity that also comes in to play. We can buy small batteries or big batteries. The bigger ones can hold more charge and so have higher AHr ratings. A 20 AHr battery can hold twice as much charge as a 10 AHr battery. If we had a fan that needs 1 amp and we wanted to run it for 20 hours, we would need at least a 20 ampere hour battery.
All this can be thought of in terms of a few formulas...
BatteryCapacity=RunTime*DeviceRunCurrent
ChargeTime=BatteryCapacity*ChargeEfficiencyFactor
Charge=ChargeCurrent*Time
Im sure you'll have more questions but all this gets simpler once you calculate a few examples. It's like pouring water into a tank, you get out what you put in for the most part
Example 1:
We have a fan that runs on 1 amp and we want to run it for 10 hours. If we wanted to use a lead acid battery what capacity rating would it have to have, and how long would we have to charge it using a charger that puts out 0.5 amps?
First, the capacity of the battery would have to be: 1*10=10 ampere hours, but we may want to oversize a little to make up for battery aging, so we buy a 12 ampere hour battery.
We have a charger that puts out 0.5 amps and the efficiency factor for lead acid is 1.4, we we have to charge for 10*1.4/0.5=28 hours, or to charge the battery up completely we would go longer.
Feel free to ask more about this as it's very hard to include all the details in one post