I have read that Dragon born is individual that is born with blood and soul of a dragon. If Vampires are soulless creatures, how is that dragon born can become vampire and still learn and use shouts as if he still has dragon soul. And if he becomes Werewolf he gains beast blood, so what happens with his dragon blood?

Vampires are not Soulless, they have souls (Notice how you can soul trap them?), their Souls are basically just the dominion of Bal