Could a human's DNA be altered so that in every skin cell they would have a chloroplast organelle? How would this affect the rest of the body?
Sea Slugs borrow genes from the algae that they eat through horizontal genetic transfer, and incorporate them into their own cells. These cells are so efficient that the sea slug can live up to 9 months without eating.
The Spotted Salamander has a symbiotic relationship with algae cells. The chloroplasts were found near the mitochondria within the salamander’s cells, meaning that the mitochondria were likely directly consuming the oxygen and carbohydrates that are created through photosynthesis.
The Oriental Hornet works a little differently. Instead of chloroplasts, its yellow band contains xanthoperin, which absorbs sunlight and builds up an electric charge that could be conducted through the cuticle of its exoskeleton, as well as through silk surrounding the hornet pupae and the colony’s comb walls. This voltage is released as current when the hornet is in darkness, and seems to be important for the development of the hornet pupae.
The Pea Aphid uses carotenoids instead of chloroplasts. Darker aphids had more carotenoids, and higher levels of adenosine triphosphate (ATP, or energy) than lighter aphids. While more research is necessary to be sure that aphids really have photosynthetic abilities, it is clear that carotenoids can absorb light and pass that energy on to the aphids.
Now for the main question, could this ability be given to a human? Since it is known that the spotted salamander is able to maintain a symbiotic relationship with algae and is able to get energy from it, it's not out of the question that CRISPR or something similar could be used to make sure that the body doesn't attack the algae cells, or even integrate the specific DNA directly like the sea slug. It would mainly be useful in the skin cells, as that's the part of the body that receives light.
If carotenoids are used instead of chloroplasts then you could end up with skin that is white and orange along with green, though the darker colors give more energy.
You couldn't live on it solely, but it could help supplement the energy received from food.
Very unlikely that only skin cells can be modified to have chloroplast, in plants, all cells have chloroplasts. The effect would be minimal except probably make people green colored if chlorophyll is made or nothing is it is not.
Photosynthesis probably won't occur unless you make it happen by modifying other parts of the cells. AFAIK the only animals to have chlorophyll adaptations only use it as a pigment and do not photosynthesize for energy. The amount of energy that an animal can get from photosynthesis is probably too negligible to give any advantage.