What problems does a CPU context switch create?

Question

ARM

As I understand it, everything is moving towards "many small but weak nuclei." Do I understand correctly that each kernel can have its own execution context?
How long does a context switch take? In the sense that if the processor (let's take ARM for the sake of interest) has 8 cores, is it possible to say that it will be able to perform more tasks at the same time (for example, servicing network connections) than a more powerful, for example, dual-core i5?
After all, in theory, on a dual-core i5, with an increase in the number of tasks, the time for switching between tasks will increase, and on an 8-core ARM, it will take 4 times less time to do the same?