The dimensions from the first reply seem great. Maybe you can try and build a separate extension for the feed and build a funnel from there into the grain storage shed. It would be extra work, but it might reduce some of the weighted stress on your original layout.
Mice usually don't attack chickens unless the horde expands considerably. But for the most part, they should be scared enough to just hide out and breed (unfortunately). I would be careful on laying down traps because you don't want the chickens to run over them. Maybe consult an exterminator...
We ran about 5 cords last winter because the snow and bitter cold temps would not go away. Almost seemed like it was below freezing for a month straight. A normal winter sees about 3 cords of wood used.