(Hyderabad, Andhra Pradesh, India)
I have read that vampires can be killed by sunlight, silver, wooden stake, fire, by tearing his head of, and using vampires disease. Will they really be killed or will they again come back on to the earth?
In the history of vampires it is said that Ambrogio was the first vampire in the world - is he still in the world or not? It is said that he was specially in Greece is this true and is he still on this earth?
Understanding the life and death of vampires is actually much more simple than understanding our own. While it is still highly debatable, there is reason to believe that humans have eternal souls that have existed before this life and will exist after. Many spiritual beliefs (including my own) believe that we return again and again to this earth in different lifetimes to continuously learn and advance our spiritual knowledge.
It's important to understand the soul's role in life and death in order to understand the answer to this question. It is well known that vampires do not have souls. That's the "curse" to being a vampire. They get eternal life in exchange for their souls. Thus, regardless of how many lives their soul may have lived before, they won't return to the system should they ever die. Of course, they will never die of natural causes, and there are only, as you mentioned, so many ways to kill a vampire. It is entirely possible for one to continue life on Earth for an infinite amount of time.
That said, if a vampire is destroyed (which is more accurate than saying "killed"), it's game over. They will not return to the earth, nor will their soul return to live the cycle all over again. They just... stop. Disappear. Are gone forever. This is why becoming a vampire is not an attractive option to most people.
I do believe, though, that this may not apply to those who are forcefully turned. Some mythologies disagree on this, but in general it is believed that one must agree to become a vampire in order to do so. Otherwise, a bite will not necessarily turn you. This is arguable, though, as there are some reasons to believe that this may not be the case, and that those who don't agree to be turned are typically drained of their blood and killed (as humans). Should the condition exist that a human is bitten, does not agree to be turned, and somehow escapes, it is still possible that the bacterial infection from the bite could turn them into a vampire. If this happens, I don't believe that this soul is beyond hope, as they never made their "deal with the devil" for eternal life. Of course, I can only speculate on such rare instances, but all signs point to the willingness to be turned as a key to giving up the soul.
As far as Ambrogio, the first vampire, or those who were turned many centuries ago, it is certainly possible that they still exist. Many myths suggest that there is a "blood hierarchy" with vampires and that by killing a vampire's maker would kill the vampires who were made by them. Whether or not this is true cannot be stated definitively, but if it is, then Ambrogio would most certainly still live as long as any other vampire were to live. If this theory is true, and Ambrogio were destroyed, all the vampires beneath him (being all of them) would also be destroyed. This could be why the oldest vampires are often hidden away under the protection of others.