Can you please explain the thumb example from the cross product reading?

For sure! It's definitely something where visual aids help.

I'm still a little confused about minFilter, magFilter, THREE.NearestFilter, and THREE.LinearFilter properties. How are they connected to each other?

It's possible in OpenGL to handle mismatch of texels and pixels in a variety of ways. See texture constants and demo

Are there examples where using LinearFilter creates a better texture than using the NearestFilter?

Let's look at the demo above!