Is a red card that can remove an enchantment necessarily a bend or break? I'm thinking of Whims of the Fates, which seems to have enough of a random component.

It’s a break. Enchantments are supposed to be a weakness for red.

Is it okay for red to remove or destroy a creature/permanent as long as it is randomly chosen from a set of several (e.g. Tyrant of Dischord, Whims of the Fates)? Is the whole issue with Chaos Warp simply that it removes a single targeted permanent from the battlefield, or do you also have a problem with red cards that remove one or more randomly chosen permanents from a set?

Red cannot do things it’s not supposed to do if it does it randomly. Red, for example, isn’t supposed to destroy creatures, it gets rid of them by dealing damage. Chaos Warp allows red to easily remove things it’s supposed to have trouble removing. To add insult to injury, more often than not, there’s not even a repercussion. (Note: Having a repercussion does not unto itself justify doing something you’re not supposed to do.)