If Christ died for all the sins of the people, does that mean everybody will be saved?

No.  Scriptures is clear that “if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved.”  (Romans 10:9).  Salvation is conditioned on man’s response.  If man does not respond to the Gospel, he will not be saved.  For God to save everyone would mean that He was saving some against their will–which goes against God’s character.