Are fallacies restricted to arguments only, or is it probable that they need not be one?

This is more like a rule that has exceptions. Also, we say "within the context of an argument" and include implied arguments, which gives it a bit more wiggle room.

In virtually all cases, it is a good idea to stick to the argumentation rule. For example, calling someone an idiot is not a fallacy, but doing so within the context of an argument then concluding that their claim must be wrong for that reason, is fallacious. Without the arguments, named fallacies usually become something else like persuasion, manipulation, or rhetoric.

Keep in mind there is also a difference between a logical fallacy and fallacious reasoning . The former is what we find in argumentation whereas the latter is much more broad.

This is an issue of demarcation. There is crossover between logical fallacies, fallacious reasoning, cognitive biases, and rhetoric. But we try to take things on a case-by-case basis. I also like to remind people that just because there is no logical fallacy does not mean there is no error in reasoning. The logical errors extend beyond mere nomenclature and categorization.

I see your point but I'm confused as to how the strawman fallacy counts as a non-argument. It's committed in the context of a debate. E.g.

Person A:  X

Person B:  You're basically saying Y. Y is false. Therefore you are wrong.

(But Y is a distorted version of X)

Same thing with the red herring, surely. That also takes place in the context of a debate.

Person A:  Why do you believe X?

Person B:  Y is very important. We should pay attention to it.

Person A:  You're right, Y is quite important.

(But Y is not the original claim/argument)

I might be misunderstanding you, but some of these do strike me as not belonging in that category.