Your a. question is unanswerable, if I want to power something that needs 12 V, obviously I'd chose the 12 V battery.
Unless there needs to be a long wire between battery and load, then I'd use 24 V, feed that through a long cable and convert it to 12 V at the load. Using 24 V in the long cable results in less current and lower losses.
What solution is "better" depends on what my priorities are. It is unclear what your priorities are to choose 12 V or 24 V so your question cannot be answered.
Regarding b: There's an online calculator here: https://convert-formula.com/ah-wh
The relation is simple, Ah is the product of Current (in Ampere) and time (in hours) that a battery can store. So a 10 Ah battery can deliver (after a full charge) 10 Ampere for one hour ( 10 A * 1 Hr = 10 Ah) or 1 Ampere during 10 hours ( 1 A * 10 Hr = 10 Ah).
Even though most people think that the amount of Ah tells you everything about the energy in a battery, they could not be more wrong!
Which battery can store more energy?
- this 10 Ah, 1.2 V NiMh battery?
- that 10 Ah, 12 V Lead-Acid battery?
Of course the 12 V battery can store more energy because even though the batteries can deliver the same current the Lead Acid battery delivers the current at 12 V, not at a disappointing 1.2 V.
To illustrate the difference we use Whr which is the product of Power (in Watts) and time (in hours). The calculation is the same as Ahr but multiplied by the battery voltage.
So the 10 Ah, 1.2 V NiMh battery is 10 Ah * 1.2 V = 12 Whr
While the 10 Ah, 12 V Lead-Acid battery is 10 Ah * 12 V = 120 Whr, 10 times more!
We can do the reverse also, a 120 Whr battery at 12 V means it is 120 Whr / 12 V = 10 Ah.