If you fit two shield cell banks then as far as I'm aware you can carry double the amount of shield cells and you can use the second bank while the first bank is still on cooldown. However I think you have to map them to different fire buttons, I think I've heard that if you use the shield-cell hotkey it will simply activate both banks.
Higher class weapons are both more powerful and more expensive than lower-class ones, however they also weigh more, generate more heat and consume more power. Grade is really redundant with weapons as a certain weapon of a certain class only comes in a single grade. Fixed weapons are more powerful than gimballed despite being cheaper, but gimballed of course are easier to aim with, gimballed in turn are more powerful yet cheaper than turrets of the same class. So in that case higher cost weapons aren't necessarily better and there is a good reason why people aspire to have a good enough aim that they can use fixed weapons. Different types of weapon have advantages and disadvantages of their own, and while generally the more powerful ones are more expensive they also have drawbacks such as slower fire-rates and expensive ammunition; and different weapons are better against either armour or shields, or at penetrating armour to reach the subsystems. Which weapon you can do most damage with depends on your skills, your ship, the opponents you face and your fighting style.
I don't know what could be causing your turrets not to fire, provided of course they have line-of-sight to the enemy.