All your questions come down to: why does our existence feel like something? Why is there subjective, personal, conscious experience? And why does it feel the way it does and not some other way?

In the following, I assume that your position about qualia deserving an explanation is correct. I don't have a fully formed opinion yet myself - I defer an explanation - but here's what I came up with by assuming your position.

First, I propose that we both accept the Materialistic Hypothesis as regards minds. In the following text I will use the abbreviation MP for the materialistic, physical world. My formulation of the hypothesis states:

1. There is an MP world which is objective, common to everyone, and exists independently of our conscious, subjective experiences.

2. All information I have about the experiences (e.g. of color) of others is part of the MP world. I can receive such information only through MP means, via the self-reporting of others. I cannot in any way experience or inspect their experiences directly, in the way I have my own experience, or in some third non-materialistic way. Symmetrically, I can only provide information to anyone else about my own experiences via the MP world. (I am not special.)

3. If we ignore subjective/conscious experience, our physical theories are a complete description of the MP world. They may be modified, extended or refined in the future, but it is reasonable to assume (until shown otherwise) that they will remain theories of the MP world only. IOW, the MP world is "closed on itself": MP theories do not naturally say anything about the existence or properties of conscious experience such as that of color.

4. MP models, and the sum of all information that can be gotten from the MP world, provides a complete description of the behavior of brains and other embodiments of "minds". IOW, Descartes' dualism is false: there is no extra-physical "soul" agent violating the MP world's internal causality.

5. MP models of brains have a one-to-one correspondence to all the conscious states, feelings and experiences of the minds in those brains. Your experience of green can be identified with some brain-state, and occurs whenever that brain state arises, and only then. (By item 2, this is unfalsifiable.)

Do you disagree with any of this?

If you accept this hypothesis, then it follows that it is impossible to say anything about conscious mind states. There are no experiments, observations, or tools that could tell us anything about them, even in principle. You can build a model of your own consciousness if you like, but it will be based entirely on introspection, and we will be able to achieve similar results by building the mirror model in MP terms of your brain-states.

Now, it's possible that future discoveries will refute part of this hypothesis - by leading to such complex or weird MP theories that it would be easier to postulate Descartian dualism, for instance. But until that occurs, our subjective experiences cannot be grounds for declaring MP theories incomplete. They are apparently complete as regards the MP world.

When you say that the color green "exists", or that your experience of green "exists", this is misleading. It is not the same sense of "exists" as in "this apple exists". I'm not denying the "existence" of your, er, qualia, but we should not use the same word or infer the same qualities that MP existing objects have.