#6) Not sure what the photo has to do with the text. However, satellites are at an (average) altitude of 22K miles and travel at a speed (average) of 17.5K MPH. So, they probably do and it's just difficult to see due to their position relative to where the moon is at any given time, their speed, and the geological features of the moon
#7) That little algebra problem does not explain its relevance to the subjecy matter
#8) First of all, that's a picture of a city through a fisheye lens which warps the image. Second, try this experiment: Find a really big ball like a big beach ball and draw the tiniest dot on it and that's about a representation of somebody's position on the earth at any given time. It appears flat because we only take up a few feet of space on an oject that is (roughly) 25K miles around
#9) This is flat out incorrect. GPS works over oceans
#10) Another opportunity to try out that beach ball experiment angain. Only difference this time is that the tiny dot is moving
#11) The word "horizon" is not derrived from the english word "horizontal" but from the greek "separating circle". "Horizo" means to divide or separate
#12) Surface tension is what makes water hold it's shape. Gravity just keeps the water from floating around in giant balls. Take a look at photos or videos of astronauts using water in space
#13) That picture does not take into account the angle in which the sunlight hits the earth. The sun hits the equater right smack at 90°. It is the direct sunlight that makes it hotter closer to the equator and cooler closer to the poles
#14) Not sure what the digging a whole part has to do with the UN flag, but it's an interesting question. However, the gravitational center of the Earth is, well, the center of the Earth. Assuming you can get through the center of the Earth without melting you would eventually find yourself going up once you pass that gravitational center. The UN flag is based on puting the 3 dimensional earth on a 2 dimensional map.
#15) See previous beach ball experiment. Also, while true that water expands (slightly) as it freezes it does not increase in surface area
#16) The same way a person standing on the rotating earth stays in the same place. Now, I'm not a pilot either, but I'm pretty sure a helicopter pilot is still controlling the helicopter to hold attitude