What is the chemical composition of a Rubbermaid Roughneck container and is it feasible for me to make my own molds?
This is a pretty broad question and might be better split into several, however a general comments on polymers, such as poly(ethylene), is that the properties of polymers can be tweaked quite a bit by control over the mean molecular mass and dispersity (probability distribution of molecular mass) of the polymer chains, as well as the addition of all kinds of stabilisers and plasticisers. Plasticisers especially may dramatically alter the flexibility of plastics. The exact composition of the Rubbermaid Roughneck is unlikely to be forthcoming.

Molding of thermoplastics by injection molding or casting is carried out by melting down plastic pellets and squirting the melt into or onto a mold. A mold release agent is often used to help get the cooled plastic out of the mold. The safety of the plastic depends on its specific composition (read the material safety data sheet for the pellets) and how hot it is (don't get molten plastic on yourself, wear protective clothing etc.). I don't know anything about the safety of mold release agents except for the fact that miniature model kits typically still have the agent on the plastic when purchased. This suggests they are fairly safe, though their presence may interfere with paint adhesion which is why pros scrub kits down before painting.

The geometric simplicity of your custom part, however, suggests that you could cut it from a plastic sheet, obviating molding and the potentially expensive equipment that goes with it.