Probably. Or maybe a less stressful commute to work, no crazy office politics, a change in diet/exercise (because you now have time to do those things properly)... It's really difficult to accurately establish correlation let alone causality when it comes to changes in one's health.
Definitely! So many things changed when I went remote that I would never suggest it's entirely down to sun exposure. It would be impossible to say definitively.
Definitely. One of many factors involved. Less commute, always getting enough sleep I am sure help a bunch. But I can also feel a big difference in my abilities when I don't get outside for a few days, even when all those other benefits stay the same.