I think you have a Ethan Allen made by Hoppe's. If you do, you are having the same problem I have with mine.
To answer your questions, the way a #11 cap fits the nipple convinces me the proper cap size is a #10. The #11s will work though.
The nipple is not a standard pistol nipple, and I don't know where you could get another one if you wanted one.
IMO The mis-fires are caused by the design of the gun, and the length of the front screw that holds the sideplate on the gun.
If you pull the sideplate off, you will notice that the front screw is threaded into the hole which connects the barrel with the nipple. In other words, it is a screw hole, and it is the flame channel for ignition.
Because my gun would seldom fire, and I'm really not into pistol shooting anymore, I didn't really persue the problem until I read your post.
Doing some measuring shows me that the forward side plate screw is so long that it reaches clear in to the center of the barrel. In other words, it looks to me like the end of the screw is blocking the flame channel.
Although I haven't done this, I would recommend filing about 1/16 to 3/32 of an inch off of the end of the forward side plate screws length. This should remove the blockage of the flame channel to the barrel.
If your gun is like mine, that will still leave over .150 worth of threads engaged with the frame and that is more than enough to hold the side plate on and to take the pressure from firing the gun.
Oh, if your gun has some "engraving" on it, it was made by the factory. If it is plain, it was a kit gun.
EDIT: Well, after trying my own medicine, I may have to revise my thoughts on the problem.
This is not to say the screw length couldn't stand to be shortened, but the poor communication between the main powder charge and the flash hole appears to be the size of the hole (at the bottom of the barrel)that is drilled into the screws crosshole.
The one in my gun appears to be only about .040 or less and it's WAY down in the bottom of the barrel. It is also offset from the center of the barrel making it a real challenge to figure a way to redrill it to a larger size (at least with the equipment I own).
Oh well, good luck to you.