>Does the level of energy the neutron hit with, decide what new atoms and therefore how many neutrons are left over?

The kinetic energy of the incoming neutron can affect which pairs of atoms are produced. Higher energies generally result in more neutrons being released, which means that different fission products must result.

>Does this mean that when they enrich uranium/plutonium, reactors are run on lower energy?

Enrichment isn't done in a nuclear reactor. Typically, something like a centrifuge is used to separate the isotopes of uranium. U-235 is a little lighter than U-238, so the centrifuge can be used to get two output streams in which one has more U-235 than the input (higher enrichment) and the other has less U-235 (lower enrichment).

I think you might be asking about something like a breeder reactor, which can produce Pu-239 from U-238, or U-233 from Th-232. There have been very few of these, because some of the neutrons are used up in transmuting one element into another (by absorption without fission), which is a technical challenge. The usual technique is to use a fast reactor (high energy neutrons), so that there are more neutrons produced per fission.

There haven't been many breeder reactors because they are more complicated and expensive to build and operate than normal reactors. Uranium is pretty common and not that expensive, so we usually just mine it and use that. The uranium in power reactors is usually enriched a little. Natural uranium is 0.7% of the uranium you would find in the ground, and it is usually (but not always) enriched as high as 5% in nuclear power plants.