Does the spine need to have separate DNA? It might be much simpler if these creatures evolved chloroplasts by themselves or by absorbing algae. What I'm saying is that if it's not a hard requirement, don't have the spine be a separate organism. Heck, even humans have ... organs which vary in rigidity based on liquid content. (I'm being as delicate as I can here)
An interesting side-effect of this might be that your creatures only keep their spine rigidity when they need/want it. They might spend half their time being soft and malleable like molluscs. Huge implications for their architecture, if nothing else.
Now moving to the hair ... Check out this page as a reference ( https://www.hunker.com/13428809/what-is-the-difference-between-needle-leaf-and-broad-leaf-trees ). Takeaway is that broadleafs are better photosynthesizers but require more water. Needle-leafs aren't as efficient as sugar production, but are way more efficient w.r.t. water loss. You might want to have both types on your people, depending on their original climate.
Further note ... don't look to photosynthesis to solve everything. It would take an impractical amount of green hair to make a person carbon neutral (ie sugar neutral as well). What it can do is stretch out the time before you starve to death. So maybe this hair evolved in an area with marginal life support, where dearth is common, and even the tiniest edge might allow you to live til the next good season. So these days, maybe the well-fed yeomen look down on those who still rely on hair-support. The most grossly spendthrift wastrels in the big cities even get buzz-cuts to flaunt their wealth!
Whoah, went off on a big tangent there. But you've got two fascinating biological ideas going on there, have fun with them!