It's enough that people in-game would notice. I mean, leather armor might only give a +1 bonus to AC, but characters will still choose to wear it rather than nothing. It might save your life. A direct stab from either a shortsword or a rapier is probably going to kill a person either way, but sometimes the rapier will kill in a situation where the shortsword won't, and there's nothing that the shortsword has going for it.
People in real life will sometimes choose a pistol based on its stopping power. Sure, a smaller gun will probably end the fight just as quickly, but the difference might matter. When you're in a life-or-death situation, there's some reason to use the bigger gun, and no reason to use the smaller one. (Or there are reasons, like concealability or availability, which actually matter. Aesthetic is not a good reason.)
Not so much. In a direct comparison, there can be right choices and wrong choices, but all of the different options are different enough that there's some reason to choose one over the other. Even if GWF might out-shine TWF in a single-target damage comparison, the guy with two swords still has the option to attack two different targets.
The important thing is, when your new character is applying to the team, that she can answer the question when it is asked. If the team leader looks at her, and actually asks why she made the choice she did, does she have an answer? Why did she choose that shortsword instead of a rapier. If your character answers that it's an heirloom and the only weapon she can afford, or that she doesn't know how to use a rapier, then those are good answers. They demonstrates the ability to make a good decision based on the facts at hand. If she says anything along the lines of aesthetic value, or tradition, or anything that doesn't matter in the heat of a life-or-death battle, then she is demonstrating foolishness and will be ridiculed for it.