I'm only on the first scenario and havent gotten any children, but all things mention are possible.
are you attempting to use the inventory to apply the bandage when you're scavenging? i dont think that's possible. Healing and recovery from sickness works best when a person is resting in bed.

Select the wounded person and click the bandage icon in your house where the bandage/ meds/herbal compress icons are located.

The meat trap, requires bait. once you choose the bait to use 1 fertilizer or meat or 1 canned food, the trap is baited, a rolling hourglass will pop up, where you have to wait a day or two for the trap to catch something. When the trap caught something, the icon changes to a piece of meat, it yields 2 pieces of meat when you send someone to collect it. but remember to bait the trap again if you want to to continue to catch more meat.

I havent had a child in the shelter yet, but i would assume, it's the same as the first response. select the child then click on the medicine or bandage icon in the shelter where the first aid is stored.

I never heard of this kind of bugs. I suggest you verify game files and unsubscribe any mods.