The deer thing is def symbolism in my opinion.

As for Kakashi's elemental affinity, he def has an affinity for lightning and water. I think this suggests his underground move isn't a simple dig move and could possibly have earth affinity also. I'm pretty sure he has used Katon jutsu somewhere, but I can't find it in the manga. In the anime they added him using the Grand Fireball right at the start of Shippudden against Sakura and Naruto.