Answer 1

Mainframes are just big computers, with a focus on being reliable and powerful.

Quantum computers are a different kind of computer - they exploit the laws of physics to allow you to solve harder kinds of problems more efficiently. Instead of sending electrons through copper wires which represent either 1 or 0, you use different physical systems (like electron spin) that can be in a combination of 0 and 1 (superposition) and that interact with each other (entanglement), which all in all results in you being able to do more stuff than a "normal" computer can do, in less time.
Quantum computing is hard, and any description with <100 words will be shit at best. However if it means anything to you, check out this: https://en.wikipedia.org/wiki/BQP#/media/File:BQP_complexity_class_diagram.svg
"P" is the class of problems which we can solve efficiently (for example, adding a list of numbers); "NP" is harder, but at least we have an efficient way to check whether a solution to an NP problem is correct (for example, finding the cheapest way of getting from Johannesburg to Moscow and back). "BQP" is the class of problems which a quantum computer can solve efficiently and as you see it can do "P" problems and more.