We see posts like this here all the time. A person upgrades to a new OS, and Font Book suddenly stops working. Usually, the problem is that Font Book's database has been trashed by the upgrade with the very common symptoms you're seeing. You suddenly can't add fonts, and fonts Font Book says are open don't appear in some, or any apps.
Restart your Mac and immediately hold down the Shift key when you hear the startup chime to boot into Safe Mode. Keep holding the Shift key until you see a progress bar towards the bottom of the screen. You can let go of the Shift key at that point. Yosemite is a bit different. Whether it's a Safe Mode boot or a normal one, you get the same progress bar. It just takes longer to get to the desktop in Safe Mode. So hold the Shift key until you get to the desktop.
OS X asks you to log in (you will get this screen on a Safe Mode boot even if your Mac is set to automatically log in). Let the Mac finish booting to the desktop and then restart normally. This will clear Font Book's database and the cache files of the user account you logged into in Safe Mode.
If that alone doesn't do it (it should), then clear out all of the font cache data.
Close all running applications. From an administrator account, open the Terminal app and enter the following command. You can also copy/paste it from here into the Terminal window:
sudo atsutil databases -remove
Terminal will then ask for your admin password. As you type, it will not show anything, so be sure to enter it correctly.
This removes all font cache files. Both for the system and the current logged in user account. After running the command, close Terminal and immediately restart your Mac.
