After Christ’s 2nd coming, is the cycle restarted with a new Christ and a new earth?

• The infinite Atonement affects worlds without number and will save all of God’s children except sons of perdition (see Alma 34:9–10, 12; D&C 76:22–24, 40–43).
• From this [Moses 1:30–33, 35, 38–39] and other scriptures we learn that, representing the Father and serving his purpose ‘to bring to pass the immortality and eternal life of man,’ Jesus Christ, in the sense of being its Creator and Redeemer, is the Lord of the whole universe. Except for his mortal ministry accomplished on this earth, his service and relationship to other worlds and their inhabitants are the same as his service and relationship to this earth and its inhabitants” (Marion G. Romney, “Jesus Christ, Lord of the Universe,” Improvement Era, Nov. 1968, 46).
• Now our Lord’s jurisdiction and power extend far beyond the limits of this one small earth on which we dwell. He is, under the Father, the Creator of worlds without number. (Moses 1:33.) And through the power of his atonement the inhabitants of these worlds, the revelation says, ‘are begotten sons and daughters unto God’ (D. & C. 76:24), which means that the atonement of Christ, being literally and truly infinite, applies to an infinite number of earths. (Elder Bruce R. McConkie)

3) Is the cycle restarted and begins all over again with a new Christ and new earth(s)?

We do not know how the cycle continues. As to what the scriptures provide we could say yes the cycle will begin again. We can also see how our Savior would remain the Savior of the new cycle of other earths, not just ours, for time and all eternity. What does the scripture mean when we are informed that Christ’s atonement is an “infinite” atonement? It could mean, infinite to the current offspring, or it could mean eternally infinite for all of God the Father’s children.

4) Does man on new earths have to start from the beginning of learning and advance or do they continue where everyone left off?

I am honestly not sure what you are specifying from this question, but will answer according to the understanding I have of this question as interpreted by me. Man on new earths are no different than us. They will start the same way as all others. They will advance through the three pillars of creation: pre-mortality, mortality, and resurrection. At least, this is what it appears to be true. Until we receive further light and knowledge as a Church collectively through God’s prophets we are left to think and decide for ourselves.

Gramps