I really don’t like the use of “reasonable” in any kind of argument. It’s most common use is to mean “you must change your mind” or “you must compromise”. It does have legitimate uses, but those seem rare.
An example of calling for someone to be “reasonable” is if they are using faulty logic, e.g. red herrings, strawman arguments, refusing to acknowledge basic facts that aren’t in dispute, etc.
Yes, of course. The term “reasonable” substantiates nothing of itself, and often tends to precede a piece of fallacious reasoning, whether the person using it understands that or not.