There's a Netflix documentary called Behind the Curve (2018). There's a guy who keeps running these experiments to prove the earth is flat. But keeps inadvertently proving that its round!
Perhaps if you live nowhere near an ocean and have no trees from which to hang a pendulum and can't afford a rangefinder for lining up two boards with holes in them.
I think you will also be surprised how hard it is to fill in the details of the experiments you are alluding to.
Also, ships do not always sink below the horizon. The right atmospheric conditions can refract the light in a way that causes them to be visible at a much greater distance than the straight geometry would allow. But this explanation can be inverted to claim that it is the vanishing that is due to atmospheric effects and that the non-vanishing ship is the accurate reflection of the geometry. Falsifying that hypothesis is, again, not so easy.
(Presumably this is also true at sunrise, so the day is longer than it "should" be from purely geometric considerations.)
No, that's not true. One can acknowledge the existence of two sides while still maintaining that one of those two sides is entirely without merit.
And in fact it is essential to do this because history shows that simply denying the existence of people with crazy points of view does not make them go away, and in fact often increases their power and influence, ironically, because the denial of their existence is actually evidence that their conspiracy theories are correct, that they are in fact the victims of prejudice.
Flat earth is an interesting case in point. It is actually quite challenging to show that the earth is round in a way that does not require you to take anyone's word for anything.