re: Variable Star?
Well, we can confidently say that stars of Solar type are non-variable, on a human timescale. Astronomers are agreed that Sol is a typical G-class star, and no G-class star has been observed to vary significantly in luminosity for intrinsic reasons, over the length scale of observation.
BUT, this says nothing about slow variation on scales of thousands of years, or longer. There *could* be a 100 Kyr solar cycle that we hadn't really seen signs of. Models of solar processes don't suggest that there should be such cycles, but the models have been developed on the basis of what we observe, so it's chicken-and-egg.
Google "Milancovic cycles" for some useful information about known periodic orbital variations that feed into climate.