What are waves (in reference to particle/wave duality)?
What are fields (in reference to electric field etc)? What are they composed of, if anything? If nothing then how do they exist? Is there any research about this, or theories?

What is matter? What is the most fundamental unit and is it "physical"? If not then how are we physical. If it is then where does it come from? Can anyone explain if inflation has any answer for this?

Are these questions all solved, or are they unsolved and unsolvable? What other questions have I missed?