When Christ returns He will take away all of the evil in the world. Philosophically we might wonder whether this is actually possible. There is an assumption that good cannot exist without evil, or pleasure without pain. It is based on the idea that we would only know what good is by having something evil to compare it to; to be able to say “good is 'not-evil'”, or “pleasure is 'not-pain'”. But this is circular because we would also need to define evil as 'not-good' and pain as 'not-pleasure'. So both “definitions” of good and evil require us to know what the concepts of good and evil mean independently of each other. When it comes to the “renewed Earth”, I must admit that what I'm going to say is somewhat speculative and philosophical. But of course, we know that God is there and that God is good. We will know God's character, and anything which is not in accord with God's character is evil. In fact, this is typically how we know what good and evil is now, in this time; (though not reliably, because our perceptions and our consciences are affected by our fallen nature, and we don’t know God as we ought). I believe that in the New Earth we will know what evil is but will simply (and freely) never choose to do evil, just as God does.
But what about "natural evils"? When things collide and break on impact, we could consider this a natural evil. But it is necessary because we cannot live without the laws of physics. Either such a world cannot exist because it would mean that the laws of physics would have to cease, or we have to say that things breaking or wearing out as a result of such laws isn't necessarily evil. I think the latter is true.
In the New Earth there will be no more death because that was a result of the fall. It's interesting to consider that in the Garden of Eden, Adam was told he could eat from any tree that he wanted to. If before the fall Adam would not die, then what purpose was there for eating? Isn't the purpose of eating simply to keep us alive? But in the New Heaven and New Earth, the Bible says that we will have access to eat from the Tree of Life, and that its leaves will be for the “healing of the nations.” In what sense will the nations need healing? What kind of a perfect world is this if we get sick or injured? Well, I don't really have a problem with the idea that people might have to eat in the New Earth. When Jesus was resurrected He ate with His disciples. Sharing a meal together is a gesture of intimacy in the Bible, and we long for what the Bible calls the “marriage supper of the lamb” where we will eat together with Christ, physically in His presence. There is more to eating than just keeping one's self alive. Apart from the social interaction around eating, we also enjoy the taste of food. But I don't really have a problem, either, with the idea that we might need to eat in order to maintain our health in the New Earth. We might think it a problem that someone might become unhealthy from not eating, and that would mean ill-health in this perfect world. However, we can imagine that in this perfect world there would be no shortage of food supply. Nobody would ever go hungry. Perfected human beings as we would be, we would neither eat too little or too much and become sick. But we are created, physical beings, and eating is simply part of our mechanics.
Will we still need sleep? I don't know, but probably – Adam slept in Genesis 2:21 (though it was an induced sleep.) Will we still need to trim our finger nails? These things we don't know, but I imagine that we will still do all of these kinds of things. But I don’t think that we will age; at least not in the sense of becoming weak and feeble. Adam lived for 930 years, even after the curse on creation had started to affect longevity. So while we might need to maintain our body (eating and trimming our fingernails, for example), I think we would always be able to do so.
Another aspect of human existence we might consider is work. Will we still work in the New Earth? Probably the best indication that we will indeed work is that Adam was told to work in the Garden of Eden, to “keep it”; (that is, "cultivate it"). So again, there’s things to manage and maintain. Farming certainly seems like a job option. But I also imagine, (again, this is speculation) that we might engage in Science, simply to enjoy the wonders of God's creation... to look into the inner workings of God's biological organisms, and to marvel at the laws of physics God has engineered. Presently we might consider that work is evil, perhaps for a number of reasons. We might hate working because it is boring and makes us tired and takes us away from the things we'd rather be doing. But even now, in this present life, we can experience (as I have personally experienced myself) that when we come to understand that we must do all things for the glory of God, including our work, then we begin to enjoy all the things that we do! I understand perfectly how it is a joy to offer up our labour to God, and that it will be for all eternity as we glorify God in all that we do in the New Earth; only far more perfectly than we do now.
So in conclusion, much of the decay of this world will be done away with - we won't age or die. But that doesn't necessarily mean that nothing can break, or that nothing can wear out. I think the New Earth will be a place for much activity! We'll build things and maintain them. We'll maintain our own bodies. I don't really see this as a problem. We were made to enjoy food, enjoy one another's company, and to enjoy our labours together. The New Earth will allow us to finally be what God intended for us to be. Just as He created birds to build nests, and we glorify God when we see how amazing they are at doing what they've been designed to do in building a nest; we have been created to glorify God in all of our pursuits. It makes the most sense to me that we will have the opportunity to build things and to practice science and medicine, and to discuss theology and philosophy. But while it's so difficult for us to understand what it might be like, it is good for us to think about it, because when we place our hope in that future we will see the worries of the present as insignificant as they are. The cares of this world will not choke us, the persecutions of others will not crush us, and temptations will not entice us.
For while we are still in this tent, we groan, being burdened—not that we would be unclothed, but that we would be further clothed, so that what is mortal may be swallowed up by life. He who has prepared us for this very thing is God, who has given us the Spirit as a guarantee. So we are always of good courage. We know that while we are at home in the body we are away from the Lord, for we walk by faith, not by sight. Yes, we are of good courage, and we would rather be away from the body and at home with the Lord. So whether we are at home or away, we make it our aim to please him. (2 Corinthians 5:4-9)