who first proposed that an atom might be the smallest form of matter, and why wasn't this
proposition made into a theory by the scientific minds of the time?

Democritus

Explanation:

Democritus was a Greek philosopher that first conceptualize the idea of an atom. He suggested matter to be composed of atoms, which move through empty spaces. Democritus explained that  different kinds of atoms have different sizes and shapes.

His proposition was not made into a theory by the scientific community of that time because there was barely little to no evidence to support the findings. The technology as a that time were not sophisticated to back up these claims.

what is the general relationship between a galaxy's distance from earth and its speed?

the answer is:

the farther away a galaxy is from us, the faster it is moving away from us.