most of the research seems to be on stuff that will be used by corporations (not affordable for common people)

To be fair, I think that’s kind of always been the case for cutting-edge computer research. The first computers were the size of a room or a small building, and only universities, governments, and large companies could afford to have one. Over time, hardware becomes smaller, faster, and cheaper, and now most people have a computer in their pocket.

Physics:

• WTF is Dark Matter?
• Where antimatter?

Chemistry/materials:

• Better batteries
• Better solar cells

Biology/medicine:

• What causes aging, and how do we stop it?
• Cure cancer
• More HHV vaccines
• Extinct malaria

Pretty good summary. I’ll add a couple corrections:

This usually involves liquid oxygen. That’s heavy and under pressure

The critical point of oxygen is below room temperature, meaning it is not possible to keep oxygen liquid using pressure alone. For rockets, liquid oxygen is typically loaded within hours or minutes prior to launch, before it has a chance to warm up and boil off.

winning solution that could escape earth’s gravity well was the Falcon 9. A multi-stage rocket with different fuels for different stages

Falcon 9 is a two-stage rocket, but it uses the same propellants (kerosene and liquid oxygen) on both stages.

Also, I’m not sure if I would call the Falcon 9 the winning solution, just the “winningest” solution so far. SpaceX’s Starship, Stoke Space’s Nova, and any of the upcoming Falcon 9 clones have the potential to improve on the Falcon 9 design or solve the challenge of reusability in slightly different ways.

quantum

larger objects

These two are kind of at odds with each other. Quantum effects are easily observable at the small scale, but rapidly become negligible on the macroscopic scale.

For what purpose? There might be an easier way to accomplish your goal.

in a way that isn’t bound by the speed of light

But also in a way that is utterly useless for faster-than-light communication.

Isn’t quantum mechanics fun? :)