2. The tides. The explanation I was given is roughly something like “the tides happen because the moon’s gravity pulls the water toward it, so you have high tide facing the moon. There’s also a high tide on the opposite side of the earth, for subtle reasons that are too complicated for you to understand right now and I don’t have time to get into that.”
The first problem with this explanation is this: gravitational acceleration affects everything equally right? So it’s not just pulling on the water, it’s also pulling on the earth. So why does the water pull away from the earth? Shouldn’t everything be accelerating at the same rate and staying in the same relative positions?
The second problem is that, when viewed correctly, the explanation for why there is a high tide on the opposite side of the earth as the moon is equally simple to why there is a high tide on the same side as the moon.
The resolution to both these problem is this: tides aren’t actually caused by the pull of the moon’s gravity per se, but are actually caused by the difference in the strength of the pull of the moon’s gravity between near and far sides of the earth, since the strength of the moon’s gravitational pull decreases with distance from the moon. The pull on the near water is stronger than the average pull on the earth, which again is stronger than the pull on the far water. So everything becomes stretched out along the earth-moon axis.
3. This one isn’t so much a problem with the explanation itself, more about how it’s framed. I remember hearing about why the sky is blue, and wondering, “ok, more blue light bounces off it than other colours. But isn’t that essentially the same reason why any other blue thing is blue? Why are we making such a big fuss about the sky in particular? ” A much superior motivating question is “why is the sky blue during midday, but red at sunrise / sunset”? I was relieved when I saw this XKCD that I’m not the only one who felt this way:
For recent times, you can also compare the dates of the C14 with other methods like counting tree rings, or the date of a total eclipse and check the calibration.
2) You are almost right. The tides are not produced by the gravity of the Moon, but from the differences in the gravity of the Moon in the water that is nearby and the average of the Earth.
You forgot to include the centrifugal force [when you are in the non-inertial frame frame that rotates like the Earth-Moon system https://xkcd.com/123/ ]. The centrifugal force is bigger in the water that is in the more far from the Moon and again the difference creates the other tide.
3) The sky is blue because the single molecules in the air disperse the blue/violet color more than the other colors. There are many ways to produce colors. In this case the light is dispersed by the whole molecule.
A different method to produce blue is using a CD to produce a rainbow and the using a slit block the other colors. Some birds and butterflies use a somewhat similar method. [Not very similar but closer to the CD method than to the air method.]
The blue in the die for cloth uses another method. You make a long chain of conjugate chemical bounds C-C=C-C=C-C=C-C, and pick length and atoms so the electrons absorb the colors you don't like and transform the energy into heat.
I'm probably forgetting a few more method, there are many of them, so it's interesting to understand which of them make the sky blue.
*) These are good questions. My explanations are not 100% complete (and probably not 100% accurate) but I hope you can fix the holes.