Yes. I think it's possible with sufficient understanding, the hard problem will dissolve.
But, the question we can ask today is: what kind of explanation would explain away the hard problem of consciousness? What is the signature the model must satisfy? I don't think there's a good answer to that.
I think that is a question more about the people to whom you are explaining the solution to the hard problem of consciousness. The natural tendency (as with 'what is AI?') is to say 'ah, but that is the easy part, the hard part is <some other thing that they feel you have not explained properly>'.
Not really, it only suggests that the brain function is involved in some way. If the brain is an “antenna” anesthesia could prevent it from functioning and that would be a totally consistent theory.
The hope for resolving this, I think, is that once we understand all processes in the brain, there will be some process that clearly is the self-referential "person" that is produced by the brain in normal operation. Anesthesia is strong evidence that there is some physical process that is the person.
The hard problem only really needs consideration if we get to a point as you describe, where we fully understand everything happening in the brain and cannot assign consciousness to any part of it, even though we can turn it off and on again (e.g., with anesthesia).