The butter does not need to be hardened. You only need to do that if you are storing it for a long period of time. You can just bring the butter to room temp to soften it and make it easier to incorporate the other ingredients. Mix it all together and place on a piece of wax paper then form into a log (if you want). You can use it right away in it's soft state or you can stick it in the fridge just like your other butter. If you are not going to use it up right away then it will last for a while in the freezer. I have a couple that I made that are in the freezer right now. One is about 6 months old.
For other flavors, the sky is your limit. With Kobe i would think you would want as few flavors as possible because part of what you are paying top dollar for is the amazing flavor of the beef. With a lesser piece of beef I could see adding other flavors, but again those flavors could be almost anything your heart desires.