This would indicate that it is one's action of belief that keeps them saved.
Jesus was clear in John 10:28 that recipients of eternal life shall never perish. I take that quite literally.
It's not our action of belief that saves us. It's God who saves us.
According to Scripture, eternal life is possessed when one believes:
John 3:15,16,36, 5:24, 6:40,47, 11:25-27, 20:31, and 1 John 5:13.
According to John 10:28, recipients of eternal life shall never perish. That means no conditions on recipients. Once one has received the gift of eternal life, they shall never perish, so said Jesus.
Since this thread isn't about eternal security, I'd be quite happy to continue this discussion in a conversation. Your call.
This actually supports eternal security. How? Because every believer is indwelt with the Holy Spirit. God cannot deny Himself. Therefore, God cannot deny those indwelt with the Holy Spirit.
See above.