It is up to you. It will totally work either way.

You could prop it by using bigger rocks - nicer than toothpicks :) Hopefully, it is unstable only because it was just repotted and the roots are not anchored well yet. The stem looks quite thick, and should be self-supporting soon.

If it is loosing it's color, maybe it isn't getting enough light? Lack of light will cause plant to etiolate - stretch; the stems will get thinner, leaves will be spaced further apart, and also change the color.

Many succulents will grow air roots, and typically there is no problem. They usually just dry up on their own, sometimes (with some plants) may grow into soil.