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Quite new to the program and I have come across the MC rendering tab. Could someone answer the questions in the title?

Monte Carlo Raytracing is a method that will, if implemented correctly, guarantee (with caveats) to converge towards a physically accurate result. It essentially simulates how light would act in the real world. Naive implementations of it are slow but these days some versions exist that are just crazy fast, capable of producing neat, lowish-noise images of fairly complex scales in seconds.
Until the initially inevitable noise has gone, however, it could take hours or even days: It basically depends on how far you want to go.
For fractal with their infinite detail, meanwhile, these methods to my knowledge, are pretty hard to get to work right: You'll often run into situations where you'd think there should be light, but it quickly becomes somewhat unlikely that light just happens to be bounced back your way and it rather tends to "get stuck". That's also where the limitations mentioned above come in. For instance, because fractals have infinite detail, there would inevitably be surface interference effects which may yield weird properties like ultra deeply saturated colors or iridescence - but with standard Monte Carlo Raytracing, such effects normally aren't considered save for specialized shaders. It would simply be too computing intensive for a technique that already is known to be rather slow.

Though the method is nevertheless quite effective as you can see in the image Sabine linked - at least if you have the patience for it! (note the render times and also that the transparent surfaces in her image aren't yet noise-free. It looks gorgeous but such artifact will take almost indefinitely to go away. The algorithm is only guaranteed to yield "the correct" result "in the limit" of infinite rendering time)

Basically, if you want very realistic lighting and have plenty of time on your hand, MC methods probably are the way to go.
It also works for quick previews: Images can be sufficiently noise-free after just a few seconds or minutes, giving you clues what to change or whether you want to go for full length.