If the heart of man is wicked, how can I protect it?

We are soul, body and spirit (our conscience). When we die "the spirit returns to God who gave it."Ecclesiastes 12:7
The body perishes but the soul is kept for judgment day.
We have a free will and we make choices, to obey the lusts of our soul or to obey the voice of our conscience. The soul that sins will die, be punished eternally, in hell.
Even though our soul is CORRUPTED we must choose against its rottenness and obey our conscience. The Holy Spirit lives in us, with our conscience, if we have accepted Jesus as Lord. still, we have the choice to obey the Holy Spirit together with our conscience or to do the
lusts of our flesh.

Can people go to heaven if they don't have a relationship with Jesus?

"Can people who read scriptures still go to Heaven if they serve Jesus yet he hardly or does not at all have a relationship yet they still preach truth of Jesus (forsake sins, make restitution when necessary, stop sinning, refute false doctrine etc.)?"

Jesus is the only one who can tell you that. Jesus said we must strive hard because the door that leads to life is narrow and few will find it. That does not leave much room for those who are not serious about following and obeying Jesus.