Chicken wire won't protect them unless it's misnamed hardware cloth. Openings anywhere larger than 1/2" diameter are large enough to let in rats and weasels, and of course mice. A weasel or mink can kill everyone in a very short time, never good.
Your cute little coop will work as a brief home for chicks or a broody hen, or separate digs for someone injured.
Build a bigger coop, buy and add ventilation to a garden shed, or reinforce a hoop coop type structure! The best coop design ever is a Woods coop, wish I had one!
Your existing run is pretty good during the day, maybe, but not safe especially at night.
Mary