chicken protection

Most certainly close the coop door. Make predators go through every obstacle possible.
Your other question - about covering their yard - well for that size it might be a good idea - would certainly give them a measure of protection they wouldn't have otherwise. It's a toss up really...freedom or security. The more of one, the less of the other. Good luck to you!

 

Is the wire in the attached "run" chicken wire or hardware cloth? If its 1/2" hardware cloth and you have fence buried along the perimeter of the run you could leave the coop open to it at night as long as you have secure latches on all doors. My run is ( if I remember correctly) 14 x 20. I used 1/2" hardware cloth for the first 4' and then chicken wire for the remaining 2' and roof, 1/2 of which is covered by a tarp. So far I haven't had any problems using it, I also buried the hardware cloth 1' around the outside.
I made a 60' circumference run like the movable pen here

http://www.utm.edu/departments/cece/idea/mopens.shtml

But I had to add 2' of hardware cloth around the perimeter ( laid on the ground & then covered) to keep the coons out, After the first winter I also added supports for the pvc that I arched over the top to support the chicken wire I used for the roof.. But that was to hold the snow load. If you just used it during the day you probably wouldn't have to have the perimeter wire.

 

Make certain birds roost clear of fencing or any area where predator might try to reach through with hands or muzzle. Birds out of reach also not as enticing as those that can at least be touched.

 

Flight top netting is great for hawks to not fly in and for the chickens not to fly out. Some guy on ebay is selling new 50'x50', 2" mesh nettings for 59.95 and free shipping, most place want 100+ for that net. It's in the mail right now should be getting it in 2 days.

 

For a coop like the above to deter most predators it would be best to cover it in 1X2 inch welded wire. Chicken wire will keep chickens in a chicken pen or out of a garden. A determined predator with time on his hands (like a coon) will just chew through it. What you want is predator wire.

Even at this a family of coons working together (one waiting quietly on one side while the others rally your chickens to the other side of the coop) can reach through the mesh and nab a "partial' chicken dinner. Consider 1/2X1 inch welded wire for your chickens safety.

By all means don't wait until the horse is out of the barn or the predator is in the hen house before you close the door.