For most of those, unfortunately, the answer is: it depends. Cortex Prime is more of a toolkit than a completed game. You can build it to play in a lot of different ways. You decide which kinds of traits characters will have and through those choices you determine how it plays. If you want more action-adventure style gaming, pick some of these traits. If you want more narrative-drama style gaming, pick some of these traits. It's a universal system so you can do most genres and settings fairly easily. Again, just a matter of the traits you want. Likewise on complexity. You can keep it dead simple with one or two traits, or fill character sheets with a dozen traits and jack up the complexity.
It's a roll and keep dice pool mechanic. The higher the die type the better you are with that trait. It uses d4 through d12. Gather up one die from each of your relevant traits and roll. You pull out any natural 1s as potential complications and total the highest two dice for your result. Compare that to a static number or a roll by the referee. Higher roll wins. There is some complexity with dice shenanigans but that's getting into the weeds.
The only things missing from your description are the difference between Plus and Prime, and Effect Dice...
Effect Dice:
When creating a trait (including damage in ranked damage modes), the size of the trait is the size (number of sides) of one of the remaining non-1, non-kept dice. Since the comparison to the opposed roll (almost all flavors use opposed rolls most of the time) is after the keep decision, one may opt to keep a higher die out of the kept pair to be able to do bigger damage.
In Firefly, this only happens for damage when one spends a plot point to not be taken out by a single hit; a variety of other situations it's suitable to use for created resource traits.
As for the differences between Cortex Plus and Cortex Prime... Essentially 2.0 and 2.1. The pre-setup flavors of Cortex Plus are a variety of different adaptations: Smallworld, Leverage, Firefly, Marvel Heroic RP, and the Cortex Plus Hackers Guide. Dragon Brigade was in development, but I don't think it was released.
Prime is, to my knowledge, not in custom use for anything I've found - the Cortex Prime core is, like the Cortex Plus Hacker's Guide, a toolkit. He-Man is slated, may be out.
Cortex Classic is a wholly different approach, more traditional... 1d(attribute) & 1d(skill), roll and total. Plot points can add extra dice, and it's still total all rolled. This includes BSG, Serenity, Sovereign Stone, Supernatural, and the Cortex RPG. (I think I'm missing one.)