Hi! It takes a long time for a bun to get settled into a new home and for him to get to know you. The nips could be his way of saying he is not comfortable being touched yet, though it seems more likely that he is nipping for territorial reasons (ie. his way of saying “get your hands outta my cage”), but either way it’s normal for a bun in a new home. He will adjust better and become more comfortable with your presence if you spend as much time as you can with him. You don’t need to pet him right away, even just sitting by his cage and talking to him is enough.
I don’t know how to get him to stop flipping stuff over, but try using a heavier water bowl (thick ceramic). You should also put a water bottle in his cage so that if he spills his water, he can still drink from the water bottle. Also, he might be trying to move his litter box if he doesn’t like where it’s at now. Try placing it in a different corner of his cage, but make sure his hay is still right by his litter box.