How to seal the hole for a spigot through a stone wall
Fill any large gaps with sanded grout in the face of the stone, let that dry, then seal the outside of the pipe to the grout after it dries with Vulkem caulking.

From the inside of the house, seal the backside of the grout with expanding foam just enough to stop any air (1-2 inches deep). After that cures, fill the rest of the 3-4 inch cavity with fiberglass insulation. Most people would just fill the entire hole with expanding foam, but that makes it extremely difficult to work on it again in the future. It's a similar technique to installing new windows, first caulk, then air seal with expanding foam, then stuff the rest of the cavity with fiberglass insulation. Try not to over stuff the hole with the fiberglass, it's the best to keep it about the same density as it wants to be naturally out of the bag. 

Instead of soldering the spigot directly to the pipe, I think you should solder a 3/4" MNPT fitting directly to the pipe, and then screw the new spigot onto those threads using teflon tape or thread sealant. This makes it easier to replace the spigot next time it fails. All you have to do is unscrew it, and screw in the replacement. It also makes it so you won't need to destroy your grout/vulkem/foam/insulation job down the road.