First point: "It is proven that the ship does not sink behind a hill of water, but that it is actually perspective which hides it."
Rebuttal: There is no "hill" of water. Water—being a fluid—finds its own level. And that level follows, nominally, the curvature of the earth's surface beneath it. To put it scientifically, the surface of the oceans and seas, either individually or collectively, will be situated at exactly the same distance from the earth's centre of gravity. This, in itself, plus the "sinking ship" illusion, proves the earth's sphericity. Flat earthers repeatedly misuse the term "perspective" to justify their observations whilst not understanding the technical ramifications of the word.
Second point: "Occam's Razor proves the earth is flat".
Rebuttal: Occam's Razor says that among competing hypotheses, the one with the fewest assumptions should be selected as the correct one, but—and this is where the flat earth reliance on Occam falls down—other, more complicated solutions may ultimately prove correct. Occam's Razor does not "prove" any two postulates one way or the other. In other words it doesn't provide any proof—in itself—that the earth is flat or spherical. Only science can prove that either way.
Third point: "The Conspiracy, by virtue of its purported existence, proves that the spherical earth model is incorrect due to willful misinformation.
Rebuttal: No worldwide conspiracy to delude the public's perception of the geometry of the earth has ever been exposed. Any "conspiracy" exists only in the collective imaginations of flat earth proponents, and is utilised simply to replace valid scientific theories that refute their flat earth hypothesis. No flat earther has yet been able to explain why a flat earth scenario would favour any particular individual and/or organisation, or, conversely, what advantages the spherical earth model grants any individual and/or organisation.
First point:
The RE model predicts that water will hide the ship bellow the horizon. To put in another way: RE predicts that the ship will go bellow our eyeline, and since the water is at our eyeline, it is therefore in front of the ship it hides (or at first, its bottom). That means, when you look at the ship with a telescope, you will just see the water in front of that ship. But that's not the case. On the other hand, the variants of the FE model predict that: a) the bottom of the far away ship will be hidden by the waves in front of it. b) the ship will become so small that its top and tho bottom can't be distinguished by a human eye. c) (EA model) simply less percentage of the light from the bottom would come to your eye than of the top of the ship. d) the atmosphere would make the bottom of the ship look too white for a human eye to distinguish it from the sea far away, but still not far enough that the top can't be distinguished (keeping in mind that both are apparently very small compared to the waves) e)…
All of those models predict that the ship would become visible by zooming the picture. And that is what telescopes do (OK, I am a bit oversimplifying this, complete explanation would include trigonometry which I don't understand either.). So, they used them to test the FET, and it proved correct again and again. Yeah, I also think that the Flat Earth Wiki is poorly written.
Second point:
Well, try and explain someone who hasn't been indoctrinated into RE that there are people walking upside down bellow us, that they are separated from us by the fluid rocks, that the sun during the night is actually not farther from us but bellow us, that we are all spinning at a very high rate without noticing it, that there are not thousands of stars (as we can see during the night), but billions of them, separated by billions of kilometers, that massive objects (such as satellites) would start flying if moving fast enough, that the moon gets its light from the sun (even though it does not appear to when you see it during the day), that, even though they appear to be the same size, the sun is hundreds of times bigger than the moon, and that we can actually see the incomprehensibly far sun even though we can't see more than a few hundred kilometers of land, that the sun actually doesn't move, but we are, that above us the laws of nature we are used to (objects falling, hot objects burning…) don't work…
I could go on forever. And even when you convince someone, you don't make him to get rid of misconceptions, you make him have more. For instance, that flying objects have something that we don't in them that can stop gravity from attracting them, that airplanes can fly without constantly correcting their path…
I've never heard that someone figured out the existence of times zones based only on the RE theory.
Accepting that the earth is round is not science, it is anti-science. Knowledge cannot go contrary to the experience.
Third point:
It is obvious why would someone want to delude the public that there are other worlds to explore: So that they can ask for money for the exploration. And, yeah, we haven't proven that NASA wasn't on the moon, but almost any of their photographs has been proven to be fake (or at least altered). So much about it. And if you are going to claim that they just look faked, but aren't (that there are some poorly explained optical illusions in them), ask yourself what is more likely.
Sorry for being so wordy, I became a FE-er only recently.