If mankind is totally separate from God then how is He omnipresent?

The separation is in the area of relationship. The picture used by the Bible is death—dead in trespasses and sin (Eph. 2:1-5). When a person dies he or she does not cease to exist. They continue to exist in the spiritual realm; however, the living cannot have a relationship with them because that is expressed through the body. The living and the dead are still present (one in the spiritual realm and one in the physical realm) but it is impossible for them to relate to each other because the body of one of them is no longer functioning. The same is true with God. Sin causes us to be “dead to God.” He is still present but we cannot relate to each other because of sin. The Bible teaches that we have to be “born again.” We have to experience a spiritual rebirth in order to have a personal relationship with God. That spiritual rebirth comes when we place our trust in Yeshua (Jesus). It does not come through reincarnation.