It's quite doubtfull that the breechplug and nipple are a single unit, I've never seen or heard of one in this application... have seen them in some others but don't remember where just now.
If you can't see through the ''flash hole'' in the nipple it's clogged... how clogged is hard to say but with what is easy to answer with the catchall: FOULING (powder, lube...). Use a piece of fine wire, the stiffer the better, as a nipple pick to clear the obstruction in the flash hole.
As far as removal of the nipple from the breechplug I'd suggest clamping the breechplug in a well padded vise to prevent damaging it and forcing that nipple out with whatever works: nipple wrench, a socket, vise grips, whatever. The nipple is nothing to be too concerned about. As I recall the original #11 nipple they come with is a simple, short affair like those on sidehammer muzzleloaders, Hawkens and the like, and easily replaceable with another like it. If I'm not mistaken the standard TC sidehammer nipple retro-fits perfectly. (I know I have both lying around in a bin somewhere!)
If the breechplug should get damaged, you have two sources of replacement breechplugs, Numrich as you mentioned and Hubbard's.
For ignition, there's the Hubbard's 209 primer holder available, the Flame Thrower style nipple in either #11 or musket cap or the basic, short TC #11 or musket nipples all of which will work in the original, the OEM replacement from Numrich or the Hubbard's replacement breechplug.
Steve