Alternative Energy

[Ruvanal]

-I wonder why, on a molecular level, the universal gravity equation does not apply.

It does. That is why your body tends to stay on the ground and not float away.

Ever wonder why our molecules are more attracted to each other than to Earth's own gravity?

Not since I looked at a basic science book of decent quality while in elementary school.

Is there indeed another force of gravity we're unaware of on the quantum level?

None that I have seen reported in any reputable science reports. There may be some wild speculation about such things at smaller scales than of the quarks, but we are far from being able to probe at those scales for testable results currently or in even in the foreseeable future. IIRC the power requirements to probe at those levels would be greater by at least a few orders of magnitude than the entire global energy output.

Why do our bodies stick together at all instead of fall apart at their molecular level and pull downward with the Earth's gravity?

Electromagnetism, see my second answer above for where to learn about this.

As I'm sure you all know, a unless molecules are bonded (ex. H2O), then they are not attached, but are merely attracted to one another. Suffice it to say, this internal attraction (gravity) is clearly stronger than Earth's own gravity. I wonder what causes it?

Again electromagnetism. You clearly do not seem to understand that at the current state of the universe, these are two different forces. And as an extra note, scientific testing shows that electromagnetism is 10^36 times stronger than gravity over equal distances.

10^36=1,000,000,000,000,000,000,000,000,000,000,000,000

https://en.wikipedia.org/wiki/Fundamental_interaction