I'm thankful you are interested in finding out what Christians believe, and I hope you'll continue to do so. One way to do this is to read the Bible, which tells us about God and how He wants us to live. I suggest you begin in that part of the Bible called the Gospels, because they tell us about Jesus, who is the center and foundation of our faith.
You are right: God is eternal and He can never die (i.e., cease to exist). This is why we can trust Him and put our lives into His hands. The Bible says, "The eternal God is your refuge, and underneath are the everlasting arms" (Deuteronomy 33:27).
And you also are right in saying that Christians believe Jesus was God. The Bible tells us He wasn't just a saintly person or a great religious teacher; it tells us that He was God in human flesh. This is a mystery we can't fully understand, but Jesus repeatedly taught, "I and the Father are one" (John 10:30). The proof is that He rose again from the dead.
But when Jesus died on the cross, He didn't cease to exist—nor do we when we die. Instead, He entered eternity, and went into the heavenly realms to prepare a place for us (see John 14:2-3). Why did He die? He did it for one reason: to become the final sacrifice for our sins, so we could be cleansed from sin and be ready for heaven. May you discover this truth for yourself.