Does it work the same way if you take oral vitamin D supplement? My skin is allergic to the sun (it hurts it bad) but I take daily vit D supplement.

It's actually a lot better. Even in countries with near constant sunlight, d vitamin deficiency bus prevalent. It's more related to our lifestyle than just geographic location.

Probably? At least in part. This study involved supplementation rather than skin production.

However, for those who can get skin production it is probably better, as there may be other effects we don’t know of. Plus it self limits, whereas one can overdo supplements.