Hi Alice Chan : Appreciate your question for supercapacitors. Regarding your first question, I would say that large capacitances at large specific current densities are favorable for practical applications. It is straightforward to charge electrodes with large specific current densities (or fast charging-discharging), but retaining high capacitances comparable to those achieved at low current densities is non-trivial and this is one of the hot topics in the contemporary supercapacitor research.
Increasing the current could potentially overload electric circuits thus proper safety managements are needed. I don't see many papers target on this topic. I would like to let other researchers with more experience to elaborate.
Sorry that I have no experience in the safety management of electric circuits. I suggest you starting a new thread to reach out to experts that can provide you professional information.