Do not know what does "speed" in healing.

Just got a "British Short Hair" increasing healing speed, don't know what is the use.

It should shorten the time that a dweller takes getting back to 100% health after a fire/radroach/raider/molerat/deathclaw event. If you just use a stimpack to heal, then the dog is kind of pointless.

I see, only inside the vault. Food is going to restore it anyway.

I never even knew that people healed on their own except when they leveled up.