Back at you.
Let's see!

"Ash didn't use Pikachu. But if he did he would've won." But he didn't so it doesn't matter since gym battles are decided between the Pokemon used in battle and not the Pokemon not in the battle.
Ash didn't use his Pikachu because Pikachu was (un)intentionally manipulated by Misty. Therefore, Misty, the opponent of Ash and then for one episode, gym leader, cheated. And because she cheated, that influenced the whole match. This isn't only about the match itself, it's also about what happened around it. The argument that Ash's didn't deserved to win this badge already loses weight because of Misty taking advantage of Pikachu decision. A gym leader would have stimulated Pikachu to fight. No, she didn't want to get obliterated by Pikachu and therefore cheered Pikachu's decision not to battle.

2. I think you need to do some bit of research. Nowhere in the anime until that point was it stipulated that the only official way of obtaining a badge would be by winning. It was only presumed to be that way by the audience, that get their presumptions and interpretations from playing the games and think it's applicable to the anime. That is like comparing a peer with a apple. Just because they are in the same category, doesn't mean they are comparable with each other. That's erroneous fallacy.

2-1 disadvantage is nothing unheard of in the anime and it has been overcome before. Also, solely because Misty's strongest Pokemon was taken out doesn't mean anything. Pikachu has been beaten in battle before but I don't see Ash losing most battle because of that.
I agree that the above mentioned example did occasionally happened during the anime, but still, that remains a assumption that Misty could have won solely based on the fact that the exact circumstances occasionally took place and the underdog surprisingly won. Gryphon came out with facts. Facts about the exact situation the battle was in before Team Rocket arrived. Facts, universally, are accepted to carry more value and weight against assumptions.

First off, Pikachu was the one that didn't want to battle in the first place. Misty did jack-**** to manipulate it. Secondly, battles are decided between the Pokemon in the battle and not the sidelines. Unless, we want to take away Ash's final frontier symbol since Brandon didn't use all of the Regi.
Difference between Pikachu and Brandon:
-Brandon CHOOSE not to use one of Regi's
-Pikachu REFUSED to battle because of Misty and her small (un)intentional manipulative tactics.

Don't overgeneralize stuff that quick please.

Except 1-0 leads have been lost and anything could've happened. Ash has gone up in battles where he dominated early but lost in the end anyway. If we want to play hypothetical situations, Misty could of surged back with Staryu.
My hypothetical examples are at least based on the solid facts Gryphon has presented in his take on the Misty fans. Your hypothetical example is based on none facts other than "Yeah, well it happened that sometimes there were these comebacks, so it could have happened with Misty.

Read that could part again. Could in a hypothetical example is tantamount to speculation.

Read above silly.]
To answer this last comment of yours, I will refrain from calling it deplorable. But seeing as you can't be convinced - even when the facts are obviously and thoroughly explained to you - then let's play it your way. So, the match ended after Team Rocket was blasted/sucked away in the water. Seeing as both parties and the third party (The three sisters) unanimously agreed after some arguing that the match was over, Ash was presented the second badge.

Now, statistically, let's see the results of the Match.

Ash:
Butterfree: Called out against Staryu before being worn-out and being recalled, but but still able to continue fighting if called out to battle again.
Pidgeotto: Called out and defeated Misty's Starmie

Misty:
Staryu: Called out against Butterfree. Resulted in stalemate before Butterfree first was recalled and afterwards Staryu
Starmie: Called out against Pidgeotto but got defeated with ease.

Results:
Ash: 2 Pokemon still battle-ready
Misty: 1 eliminated and one still battle-ready.

Ash therefore - according to the statistics - deserved the second badge in accordance to the unanimous decision made by all the parties at the end of the episode that the match was officially over.