I've noticed some of my dwellers getting grey hair. Do they ever die? How does their age effect their stats? If they don't die from old age, I think they should. It will be heartbreaker to lose a dweller I've spent so much time training, but it would add some spice and keep the game interesting too as dying dwellers would effect the game balance constantly.

Nothing I've seen or read seems to indicate that dwellers age. Sure, there are greyhaired and bald dwellers, but if you took notice of them as a child they were already grey and bald then (bit silly I think). So this is purely cosmetic.