Ahah, Thank you for your feed back !
For the hen : the children take care of the hen, so if they all die. The hen will kill you. The right solution is to carry the hen to the burrow.
For the UI : We had some ideas for UI, but we prefered to finish the game and have a complete gameplay. That's why there is no transition and no background in our inventory screen.
If you want the solution there is a walkthrough here : https://pastebin.com/raw/rDpjaGRT