Fallout – In Fallout Shelter, How Fast Does Radiation Heal without RadAway

The only thing which could explain it (besides a bug) is that you may missing some electricity or water. If you haven't enough electricity your food and water supply will fall down and maybe collapse. This will increase the radiation of your dwellers. In some cases they may die on this.

Otherwise, I would say it could be a bug. I've had a situation which was nearly the same. In my case electricity was too low, which leads to the situation I described above.

It depends on what you want the explorer to do. Strength lets them kill things faster. Perception helps them find opportunities for caps, XP, and loot. Endurance and level provide more HP, allowing them to survive longer on the same number of stims. Charisma makes it more likely they will resolve situations with strangers in a more positive light (gain more XP or caps, lose fewer HP). Intelligence makes them run away from combat faster, losing less HP. Agility lowers the damage they take in combat. Luck helps them find better loot and more caps.

As far as which to prioritize, Endurance, Luck, and Perception are most likely to get you better gear and more caps, but eventually having an explorer with straight 10s is good. Also note that while dwellers can be trained up to a 10 in each SPECIAL stat, the bonuses from outfits stack and provide benefits beyond a 10. For example, having 11 or more Endurance makes the explorer practically immune to radiation. (There is speculation that the radiation immunity may not have been intended and could be nerfed in a future patch)