Can explain those passages in context? The Bible isn't a bunch of proof texts. Everything that is written is written within a certain context. If we're just going to pull a sentence here and there we can claim the Bible says just about anything we want. What you didn't post were the conditional verses that were also spoken. For instance, Jesus said some believe for a while and in time of temptation fall away.
Notice how eternal life works.
25 Jesus said unto her, I am the resurrection, and the life: he that believeth in me, though he were dead, yet shall he live:
26And whosoever liveth and believeth in me shall never die. Believest thou this? (Jn. 11:25-26 KJV)
Notice that the "shall never die" part happens after the resurrection. So, in the mean time while we're alive we need to make sure we don't fall away.
Notice that the one who believes did die. So, eternal life begins at the Resurrection.
1. God does not just say things to waste his breath, if he says them, we should trust what he says
2. John 3 is about being born again, IE. Born spiritually from above, Jesus tells nicodemus, unless he is born again, he can not enter the kingdom of God. And he tells him how. Whoever believes, is not only made alive. But we are told how long he will stay alive (eternal)
3. John 4 is jesus explaining to a woman that drinking water from a well is good. It sustains our lives a d nourishes our bodies (a body can not live without it) and a true fact. Whoever drinks of that water will thirst again, but i it not better to ask for the water that will let us live forever? (Ie.they will never thirst again
13 Jesus answered and said to her, “Whoever drinks of this water will thirst again, 14 but whoever drinks of the water that I shall give him will never thirst. But the water that I shall give him will become in him a fountain of water springing up into everlasting life.”
John 6 is the same
Don’t search or work for food which perishes, but for food which will endure to eternal life. Which Jesus will give. As he said, whoever eats of them food will live forever. Never hunger or thirst, never die. HAS eternal life and will (not might) be raised by him on the last day (is being delivered to him at judgment day)
1 John is specific. He wrote all he write to prove to us we have eternal life right now. And by this knowledge we will continue to believe in hm.
As for the passage you used. It supports what I said, Whoever lives and believes in me shall never die. This is called eternal life.
Remember, John said whoever sins has never seen or known God. Whoever has been born of God can not sin (a lifestyle of living in sin) People who are born of God are those who obey his commands, These are descriptive passages, who the people of God are. Not prescriptive passages, which tell us how to be given eternal life.
Eternal life is forever. Never ending. John said we have it, Jesus said we have it. Paul said our hope is based on this promise, which God made before time began.
Conditional life is not found in scripture, unless we are talking about temporal life on this earth.