Frame Challenge: Assumptions are being made in the question regarding DNA modification being a kind of magic.
Pretty Much a Normal Diet
It's a pretty common sci-fi trope, but DNA modification isn't magic. If the DNA in every cell in your body changed to that of a capuchin monkey right now, it would be some time before you noticed anything, and it wouldn't be that you turned into a capuchin monkey. If you change your DNA, your body is still what it always was. Changes made to germline cells (sperm, eggs) will change what the offspring develops into, but an adult organism cannot be transformed by changing their DNA.
What is likely to occur if you dramatically change the DNA of an adult organism is that they will die. DNA mostly codes for protein synthesis. 1008
If important proteins (for the adult organism) are excised or omitted, the organism will die before any changes to their appearance occur.
If your species wants to live in the bodies of other species, they would have to grow a cloned body of that species, and then somehow transfer their intelligence into it. This was a plot point in a lot of <PERSON> works.
Mobile organism (typically human) photosynthesis has been covered on this StackExchange before, and the consensus is that even if you could expose all your skin to the sun (unlikely, since you need it to keep your insides in), it was perfectly sunny every day, and you didn't exert yourself, photosynthesis provides about 25% of the caloric energy necessary for adult human operation. Even if you "optimized" photosynthesis (difficult to outdo evolution in that regard) with DNA editing, bettering that performance is unlikely.
Similarly, for a non-sessile organism, extracting energy from wind or impact is going to provide a vanishingly small portion of the energy the organism requires. Extracting energy from warmth may actually be impossible for exothermic life, because it would violate the laws of thermodynamics.
Where your DNA-modifying race might come out ahead is optimizing intestinal flora and digestion to break down foods more efficiently and synthesize useful proteins, allowing (for example) a wholly plant-based died comprised mostly of sugars to power their metabolism. But that sounds kind of boring for any chefs in this society!
Edit: Dug into this a bit further, and if you dramatically change the DNA of an adult organism, they die very quickly. Within minutes, of massive anaphylactic shock and hemorrhage, as cells disintegrate. 258