Is crushed rosemary the same as minced rosemary?

Yes. Many supermarkets and strip malls use rosemarry as a decorative plant becasue it is easy to maintain and gives a nice floral smell. Often you can find this plant growing outside...

No, they're entirely different plants.

No. Myrrh is the gum resin from any of several trees in the genus Commiphora.Rosemary is a bush from an entirely different genus, Rosmarinus.

tablespoon fresh rosemary equals 1 teaspoon dried

No. Crushing results in a fine pulp. Mincing gives you finely diced pieces. The difference shows up when you cook it in oil. Since crushing results a more moist product, it will make the oil spatter...