You want to wait until the skillet is ripping hot before you drop the steak in. I usually wait until I'm ready to finish cooking before dropping the butter in. Butter burns quickly so you do not want the butter in there for a long period of time.
Yep.
It also boils out the 15-20% water content of butter to make it closer to 100% fat.
Once you remove these (water + proteins and other impurities) the smoke point is much higher and it is much healthier for hot cooking.
It is called "ghee" when done at medium high temp, which gives it a slightly darker colour and nuttier taste (Indian way I think), and just called "clarified butter" when done at low temp.
Other advantage when done properly -> it does not go "off" anymore and does not need to be kept in the fridge, so you have this much easier/softer substance that you can spoon out of a jar.
You can even use it for deep frying - honestly the best fat for it.
