Dear Cieza,
I just realized I may not have answered your question in my quest to get to the real issue. So here goes:
Question 1: Would I still believe that Christ died for the sins of others, if it were proved that heaven and eternal life do not exist?
Answer: Yes
Reason: I think you have brought up a vital point here. Your wording is "...believe that Christ died for the sins of others." By others, you infer that when Christ died He was dying for His sins.
1) Christ did not sin because He is the Son of God. "But unto the Son He saith, thy throne, O God, is forever and ever; a sceptre of righteousness is the sceptre of thy kingdom.Thou hast loved righteousness and hated iniquity (sin);therefore God, even thy God, hath anointed thee with the oil of gladness above thy fellows.And, thou, O Lord, in the beginning hast laid the foundation of the earth, and the heavens are the works of your hands." Hebrews 1:8-10
"In the beginning was the Word, and the Word was with God, and the Word was God. All things were made by Him, and without Him was not anything made that was made. In Him was life, and the life was the light of mankind." John 1:1-4
"And the Word was made flesh, and dwelt among us, and we beheld His glory, as of the only begotten of the Father, full of grace and truth." John 1:14
"Seeing then we have a great high priest, that is passed into the heavens, Jesus the Son of God, let us hold fast our profession. For we have not a high priest which cannot be touched with the feeling of our infirmities, but was in all points tempted like as we are, yet without sin." Hebrews 4:14-15
See, Cieza? The Bible claims that Jesus is the Son of God, that Jesus is the Creator, and that Jesus was tempted in all ways we are, yet never yielded. That brings up a reason for me to believe that His Word is true.
Remember when He was arrested by the Jewish leaders? They tried Him, sent Him before the Romans, and then beg and pouted until Pontius Pilate gave in and crucified Jesus. They beat Him, and spit on Him, tore out His beard, and mocked Him. And with that crown of thorns on His head, they laid Him on a cross of wood, nailed Him to it, and stood it up, and with a "Thunk!" it fell into the hole dug for it, ripping and tearing at the Lord. But the most interesting thing that happened, Cieza, is that a few hours later, after all this abuse and fiendish torture, Jesus DIED! We now humbly bring in the governing law for this matter: "For the wages of sin is death..." Romans 6:23. But the Bible says, as I have quoted a few instances of, that Jesus never sinned in word, thought or deed. So when He looked up to Heaven and said "It is finished. Father, into Thy hands I commend my Spirit." And died, He was not dying for His sins, because He didn't have any to die for!!! He was dying, loaded down with the sins of all those people that would, through history, repent and believe in the Christ unto salvation. Then He spent three days in a tomb. On the third day, Jesus rose up from the dead (He was truly dead) and revealed Himself to His disciples. His rising from the dead proves that He did die for our sins, Because if He was dying for His sins, He could NOT have come back to life ("The wages of sin is death") .But He did come back to life, after having destroyed and abolished His people's sins, so death could not hold Him, legally. You see, God did all this legally and aboveboard so that an honest sceptic like yourself could be shown the reasonableness of God's entire plan for the salvation of those that repent and believe.
Sorry if I overloaded you answering your FIRST question...if interested, I will try to be briefer in the future.
Julian of York.
"For thou art worthy, O Lord, to receive glory, and honor ,and power; for thou hast created all things, and for thy pleasure they are and were created." Revelation 4:11
PS He also said,"I go to prepare a place for you. And if I go, I will come again and receive you unto myself, that where I am ,there ye may be also."
And on that promise, Cieza, I rest my eternal well being. My faith is not CONDITIONAL...It is COVENENTIAL. I am relying on my Covenant relationship with God. He made the promise, and I believe it.