11 Hens, Missing Tail Feathers, 9 Eggs, Rooster?

Can you post pictures of all of your chickens? I think you would be able to tell if one looked different, but a 2nd opinion is always good. Also, roosters don't always crow just in the morning.
The missing feathers could be due to something else, though.
Anyway, I'll look at the photos and I can tell you if you have a rooster.
-M

 

This is a photo of my rooster at a couple months old. Maybe 4 ish. Notice the tail? That's what you'll start to see in a rooster. If you compare the tail to the tail of my BR, in the foreground, you can see a difference.

 

Welcome to BYC!

Depending on the breeds of your birds production levels can vary considerably and getting 9 eggs a day out of 11 birds is actually very good. Generally speaking, even the most productive breeds average only 6 eggs a week, so getting an egg out of every bird on any given day is not the "norm". Also, missing feathers *can* result from mating, but there are many other potential causes that have nothing to do with gender.
If you post some photos of your flock we can help you assess gender - as well as offer some input on the missing feathers.

 

There is no way of knowing, without seeing pictures of your flock. I have roosters, and my hens still have their tail feathers. You may want to check your chickens for lice or mites. Not every chicken will lay an egg every single day. I don't always have the same amount of eggs as I do hens every day, either. When you get a chance, post some good, quality pictures of your flock (good, clear pictures of head, combs, wattles, hackle feathers and saddle feathers will be helpful.)