While certainly possible, humans have nowhere near the surface to mass ratio to produce any significant portion of their food via photosynthesis. So i'd be pretty pointless. Now, if there's a lot of sun input, and not a lot of energy used, it might make a difference. But we're talking hibernation sleep out in the open in the middle of summer here. Sunlight has an intensity of about 1kW per square meter, measured at a surface perpendicular to the rays. Now, photosynthesis can use around 10% of that, at best. (hard limit)
Which means, that with a surface area of about 2m² (big person), and really great efficiency, sunbathing could generate about 180 calories with an hour of full light. Now, in the Sahara, you could power a sedentary lifestyle with photosynthesis, but anywhere with clouds, or during winter, or where you're not in full sunlight, and it hardly matters.
On another note, photosynthesis could provide calories (starch and sugar) but it can not provide other required substances, so unless there is some really great closed-loop system in the body recycling those, some food would still be required.
As an aside, a person generating all their energy from photosynthesis wouldn't need to breathe. Shouldn't breathe in fact, since exhaling CO² means losing carbon, and photosynthesis can't generate that from nothing.
Alternatively, they could do like plants do, and have two different metabolic processes running, in daylight exhaling net oxygen and absorbing carbon dioxide from the air, and without light, exhaling CO² like everything else.
Roots have nothing to do with photosynthesis, they're just big webs which absorb various substances from the ground. No reason why a person or some exotic animal couldn't use them, besides the obvious: those roots need to be in the ground, which gives one the mobility of a tree. But something like a bunch of root-like appendages which are used to absorb various substances from bodies of water would be plausible. Or at least possible.
Skin color would be relatively arbitrary. Whatever portion of light doesn't get absorbed determines colour. Photosynthesis absorbs very narrow lines of radiation so the color still mostly depends on pigment. What part of the light gets actually absorbed is determined by the exact chemical photosynthesis process that takes place (there's more than one possible).
Even white (as in paper-white, not the pinkish skin-white) is theoretically possible, if the photosynthesis works at a very low efficiency, and enough light is still reflected to make it look white. That's counter-productive of course.
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