CPU core question
Separating a CPU into multiple cores is basically adding redundant sections and controller logic, cache, etc. There are many sections that serve different purposes and instead of making a giant one of each, making multiples of each one would give you what we call a multi-core CPU. The benefit is that these cores, since each one has a complete set of everything it needs, can run calculations independently instead of dedicating the whole CPU to a single task. Having a dual core can be similar to 2x 1.6GHz processors but it depends on the task at hand.
If you had your computers calculate Pi to the first 1 million digits, they would finish at the same time; however if you had them do the task twice, the dual-core would finish twice as fast (and would take no longer than doing it only once) because it can do them concurrently, while the single core would have to do them one at a time. That's a simplified example but you get the idea.
The real world benefit is rarely 2x performance with 2x the cores, but somewhere inbetween, and the level of benefit depends on the type of task. Complex programs that need a lot of CPU resources are usually programmed to split their calculations into multiple threads if they can, so that multi-core CPUs can complete the tasks faster but depending on the program that is not always possible (for example if each calculation in a series requires the results from the last calculation, that cannot be split into multiple threads so a quad-core will take just as long as a dual-core).

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