Concerning the curvature of space: If you measure sum of angles of triangle on the surface of earth, it will be grater than 180 deagrees thanks to positive curvature of earth surface. For triangle in your backyard the diference will be immesurable, but if your measure traingle with segments spanning for 6 thousends kilometers sum of the angles will be closer to 270 deg than 180 deg.
For the spacetime in the vicinity of earth you don't have to necessarly think about large distances, here (https://www.reddit.com/r/askscience/comments/2pu2o0/is_there...) someone calculated diference for two clocks so you can se scale :
"If so the clocks on Earth's surface and 7km down would see a relative drift of 0.001ns per second, so the lower clock would tick that much slower as viewed by someone on the surface. At that rate over the course of a billion years the surface clock would pull ahead by 525.6 minutes."