1. The author uses the argument that stone is heavier (e.g. denser) than water and is therefore not pushed outwards by centrifugal force. This is wrong as centrifugal force is proportional to mass and therefore acts on stone as much as on water. As the earth was formed, said stone was liquid, thus there is land at the equator.
2. You are not able to see the actual curvature. You are able to see things vanishing behind the horizon, which is a phenomenon of curvature.
3. Because earth is huge. Also, we have. Raindrops, for starters. Experiments on the ISS (okay, they get denied). I think rabinoz posted a picture of water in a spinning barrel, which sticks to the (curved) wall.
4. Easy: In....Out...In....Out...
Regarding the question: The pressure slowly fades with increasing height, there is no sudden "pressure - no pressure" border. Also, negative pressure does not exist. And the example with the box is comletely wrong, as the air is not sucked in, but pushed in by the outwards air pressure. Therefore the air pressure at a certain height is always exactly high enough that the upwards force caused by pressure difference gets countered by gravity.
5. Neither. Earth is huge, Sun is orders of magnitude bigger and really, really far away. Don't remember the exact question, though, you might want to elaborate.
6. It does not. I think this question is concerning crepuscular rays. The author lies about the explanation, they are explained by perspective. There have been several threads here.
7. See MaNaeSWolf
8. It is not. Don't remember the exact question, though, you might want to elaborate.
9. The earth. Don't remember the exact question, though, you might want to elaborate.
10. It is not. Don't remember the exact question, though, you might want to elaborate.
11. Because of those pesky stones flying through space. The ones that sometimes also hit earth. Don't remember the exact question, though, you might want to elaborate.
12. There are permanent hills, mountains and valleys in the ocean, though they are not noticeable by the naked eye. They have been revealed by satellite observations (those things FE-ers deny). But I think the answer to the author's question is simply that water always stays level.