1. Fairy Tail is a fantasy shonen to entertain, it has nothing to do with reality [outside of using names of actual gods and zodiak signs]
2. Anime is entertainment, real magick energy you cannot see but feel, real magick is actually pretty boring. No fireballs or transformations.
3. Dragons are not physically real.
4. Astral dragons are like spiritual energy. you cannot kill an astral Dragon [as far as I'm aware]
Study real magick if you are interested but trust me, it's not as glamorous as Fairy Tail. Dragon Magick is the belief dragons are from a spiritual plane and can guide us and assist in spell casting [similar to calling on a deity] they are not physically real, you cannot and do not go around slaying them, nor can you gain a dragons power and become one.