Abdullah,
You obviously haven't read the forums I suggested you read with the answer to all your questions. You will find these questions answered there. But yes!!! Jesus did exist before Moses.. Read John 8:48-58 for example.
Jesus and the Jews are discussing Jesus' claims that anyone who believes in Him will never see death. (this followed an earlier discussion in the same chapter, where they have heard him declare He is one with the Father.. God! They are now asking if He is demon possessed over such claims). The response of the Jews is this
Abraham died and so did the prophets. .. Are you greater than our Father Abraham?
Jesus declared that Abraham in faith looked ahead and saw Jesus and knew He was coming and rejoiced. The Jews then asked the same sort of question as you have asked in your question "You are not yet 50 years old and yet you have seen Abraham."? Jesus replied with some life changing words if you believe them.
Before Abraham was I AM
He used the very name God had used when He spoke to Moses at the burning bush. Moses asked God what he should say to the Israelites when they asked who had sent him to Pharoh to ask for their release.
God replied
"I AM WHO I AM This is what you are to say to the Israelites I AM has sent you."
He furthur declared "This is my name forever, the name by which I am to be remembered from generation to generation."
When Jesus declared those words.. "Before Abraham was I AM" the Jews knew exactly WHO He was claiming to be. This was God Himself.. Deity speaking or else this was the most horrendous act of blasphemy.
Now notice, John describes Jesus as being surrounded by angry, stone wielding Jews who are out to stone Him for blasphemy. The scriptures say
but Jesus HID HIMSELF, slipping away from the Temple Grounds". Hmm Omniscient, Omnipotent God wouldn't you think?