cable size vs current rating
There is not really such a thing as current rating for wire. The practical limit is wire temperature. At a certain point, the insulation will melt or burn. Extreme overloads can melt the wire, but that's a different problem entirely. Without knowing your application, or how the wires will be bundled and routed, it's not possible to say what wire gauge is appropriate. In certain applications, such as residential wiring, tables exist in regulations to remove guesswork and ensure that no installed wires will get hot enough to start fires (if properly installed). Wire sizing in regulations is typically extremely conservative.

One conductor is preferable to two for power transmission. Think about this: you have power transmitted over two wires in parallel. One wire comes loose. Now the current is only flowing through one wire, and it may get dangerously hot. If you only use one conductor, the system will fail entirely if a connection opens. This is a safe design practice. 

You can ensure that wire will never get dangerously hot by protecting it with a fuse or circuit breaker. The size of the protective device will vary depending on the application, available cooling, and normal load current.

Solid-core wiring and stranded wiring will do the same thing, but stranded wire is much easier to work with. Solid-core wire is more susceptible to breaking when flexed.