1. Eh, I can't refute or necessarily explain the fact that you can't see something, but if I can see it and the scientific establishment says it's supposed to be there, then I have every reason to think the problem is with you. That's maybe not much of an argument for the Earth being round, but if you're just asking a question, then I'm fine just answering "well, I can see the curvature, so maybe it's something wrong with your eyes?"

2. Okay, describing lighthouses as specifically designed to send light over the horizon was an exaggeration and they'd be designed differently if that was the main goal; they're intended to send light as far as possible but that mostly means being visible at medium distances through bad weather, being visible over the horizon on clear nights is a useful side effect. The point is, powerful directional beams of light are visible over the horizon. Also, between the height of a shipboard observer and the height of the top of a lighthouse, some ships might simply have direct line-of-sight to some lighthouses over 20 miles' worth of curvature.

3. The first problem with that theory, and there are lots of problems with it, is that "Density" is a scalar quantity and not a force.