Not quite, they describe different things, so you can put them on the same scale. Classical mechanics is a framework for describing the dynamics of a system once you specify the forces. QM is a different framework. But GR is a theory for describing a particular force, gravity.

This doesn't make any sense IMO, unless you can come up with something to back it up. If you mean the precession of a top in the presence of gravity, then sure it can be solved analytically in classical mechanics, but the general two body problem has no analytical solution in GR, and I doubt the restriction to a top simplifies it enough to allow a closed form solution. But I can give you valid examples that suggest the opposite. In classical mechanics, the dynamics under a linear potential (constant force) is very simple: constant acceleration in one direction. But try solving that in quantum mechanics, and what you get are hideous Airy functions to describe the position of the particle.

Not even then. I don't know what it means among laypeople, but for a physicist TOE means a quantum field theory that describes gravity, electroweak and strong force. I can guarantee that we will have such a theory in 100 years, and probably a lot less. I can also guarantee that this TOE will eventually be superseded by a more accurate theory.

Nope. It is just that scientists use simple models like harmonic oscillator for most systems, simply because they are easy to solve. That doesn't mean that the universe is 'built' from second order laws. The rest of your post is also similar misinterpretations of QM, optics etc