Is the total resistance of all the parallel loads more than the smallest individual resistance?

No. Perhaps an analogy would help understand the answer to this question.

When you are at the store, and you are in a line waiting to be paid, opening up another line or more should increase how fast people can move through the store. That is a parallel operation. (If you have to go through one line at the store and then go through another line at the store, that is a series operation).

Similarly, when a current meets a resistance, putting additional resistance in PARALLEL allows some of the current to divert to this new path or paths, allowing more current to flow through the combination of resistances. Since more current is flowing though the combined resistances, the equivalent resistance is less since less resistance always means more flow.