What produces more power on Earth and is more efficient at energy production, steam powered turbines in coal/nuclear power stations or solar panels??
Per unit mass, per unit area, per unit fuel, or per unit entropy? This is a rather mportant distinction. While steam turbines are produce more power per unit area. They are, however, far more massive than photovoltaic panels of comparable output, which is why photovoltaics are used on space-stations and satellites these days.
In space there's no Earth gravity affecting the turbines meaning they will move even quicker and more effectively than in a gravity environment, obviously therefore producing far more power output.
Not relevant. Friction is the limiter, no gravity.
In the case of the batteries you only need fuel to transfer the batteries to and from Earth and with it being in space you don't need a lot of fuel to do it. You therefore produce more energy and use less fuel than you would with an Earth based system.
You save fuel, have a free energy device creating as much power as you want depending how big you build it and simply transfer that stored energy.
Batteries large enough to make such a project worthwhile would also have so much mass as to make moving them in any reasonable time insanely wasteful.
It's logical to assume that in 1 year the space based powerplant would produce more power for Earth or colony than inefficient solar panels.
Possibly. It depends on size.
Back to the original question, you can boil water using sunlight on Earth. Understand that the temperature of body is determined by its thermal energy*its specific heat capacity / its mass. The thermal energy absorbed from light is determined by the output of the light source / the distance from the light source^2 * the absorbance of the body * the surface area of the body.
Add wattage gained and subtract wattage lost due to radiation, conduction, and convection (you can look up those equations yourself). So long as the result is a positive number then body will continue to increase in temperature.
Large commercial solar plants on Earth tend to be solar-thermal rather than photovoltaic, because bulk solar thermal is both cheaper and a more efficient use of space. But this only applies when economies of scale set in. Photovoltaic is both cheaper and easier for powering small objects and individual homes. In the consumer market solar thermal is almost exclusivly used water-heaters.
Essentially, a space-based solar thermal plant loses on mass and always will. Its extremely heavy and will require a great deal more propellant than the equivalent solar panels will.
Also, space is not cold. Seriously, it isn't. Vacuum is the best insulator there is. This is why spacecraft of all sorts need giant radiators.