I think what you're calling "bad faith" is either (a) an attempt to avoid the fumbles, which is simply IP Proofing made extremely necessary, aka standard optimization tactics; or (b) an attempt to show the DM exactly why a critical fumble rule is bad.
No. What I call bad faith is people who jump to the barricades simply because a DM want to use a rule which lower their mechanical ability in combat. I see it happen way too often on those boards and it is not really surprising since so many people seem to hold the mechanical aspect of the game as an immovable force of the universe. Using sarcasm in a humourous attempt to completely dismiss the case only because it is convenient is also both bad faith and ignorance in my book.
There are lots of houserules which lower peoples' mechanical ability in combat. Here are 3 reasons people jump to the barricades for critical fumbles in particular:
1) It worsens mundane characters while not making any difference to spellcasters, who are already far superior than mundanes.
2) Because it's a flat 5% chance per die roll, characters who make more attacks (i.e., more powerful characters) will be more likely to fail than weaker characters. If you create a god of combat who makes 20 attacks per round, that means that on average that character will be critically fumbling once per round, compared to a 1st-level warrior who will critically fumble once per 20 rounds (or every 5 combats per so), which breaks verisimilitude in half.
3) Less importantly, there are things one can do to mitigate crits; however, fumbles aren't supported in the rules, and the DMs who houserule them rarely create materials for PCs to mitigate fumbles.
I have no problems with people trying to find ways to lessen the problem as long as it is a legal way in the system. As a matter of fact, I do remember there is a feat in complete soundrel which turns your critical misses into critical hits. I don't know if it was mentioned in this thread, might be interesting for people to check.
No, it only works on saving throws.
On the other hand, I'm a DM who use fumble rules too. And the players like it instead of the opposite. Why? Well, first I don't use a single result for a fumble. The char dropping his/her weapon is indeed a classic, however I also use a plethora of other results which add up and spice up the game. For example, the char in question might loose footing and drop on the ground instead. Sometimes, rarely, I unstrung a bow for an archer (only requiring a complex action to restring) but most of the time I ask the archer in question to roll a directional D8 and see if he/she hit a friendly instead. Otherwise the shot just go loose. Sometimes I simply use my imagination and write up an original reaction on the stop. Oftentime the current situation will scream out for a particular humoristic fumble and I'm always happy to oblige.
So you just make something up when a player fumbles? That has a couple problems, namely (a) it depends on DM skill, so what works for you may not work for others, and (b) it's impossible for a player to predict what can happen, so they can't take steps to mitigate it, so your random effect could arbitrarily lead to PC death.
A) Possibly true but a good DM need to be able to improvise. Otherwise the DM in question will never be really 'good'. PCs never do what the DM think up, or do it differently. A DM should already be used to do that all the time.
Which is why it depends on DM skill.
B) Being impossible to predict is precisely the whole point. What would be the point of criticals if it wasn't to have a rare but unpredictable event possibly changing the whole battle? Can't an unlucky PC also already die from a lucky crit plus maxed damage dice from a strong monster? Isn't the whole point of going adventuring (as a whole, as in why the char in question has choosen to be an adventurer in the first place) not knowing what you will expect versus, I don't know... Staying home as the town blacksmith?
Anyways, my simple answer to point B is this: if we didn't want the game to be random in the first place, we would not be using dice. The whole point is not to know in advance what would happen. Otherwise it would be a story in which you participate on the side, not a real personal adventure.
This isn't really an argument... lots of things in a campaign are unknown. And yes, an unlucky PC can die from a crit from a monster. It's much more interesting and heroic if the hero dies that way than because he slipped and fell and broke his neck. If that kind of thing works for you and your gaming group, then great! I'm not telling you how to have fun. But don't use that as proof that critical fumbles don't make the game worse for most people, particularly anyone who doesn't play a spellcaster.
It is always fun when players start remembering encounters by memorable dire moment they managed to get out of.
And of course, what balance everything back in the end: the monsters fumbles too. Players stop whining when they realize that the monsters fumble more than them simply because they are more numerous in a swarm or when a big, strong monster fumbles and open strike possibilities they would not have otherwise.
There are a lot more monsters than PCs. And the PCs only have to die once.
EDIT: The "critical on 1" only means that you miss, not that you then have to mess around dealing with other problems.
Can creatures be immune to fumbles like a monster can be immune to critical hits? Can a player enchant their armor or weapon with something that gives them a 25% chance to negate a fumble, just like Fortification? Does the player have to confirm a fumble like they have to confirm a critical hit?
I am sorry, but I do not understand your comment about dying. Yes monsters die all the time, but PCs can die too? Or is it that PCs never die in your games? There is various ways to bring a character back to life. Once again, the game would not be as interesting without the risk involved and having nobody in life threatening danger (or at least having his interests threatened) during a whole campaing is a sure way to make it going dull.
Of course PCs should be able to die. But again, they should die doing something important rather than from dropping their sword on their femoral artery.
The point of playing a PC is to be a hero in an epic story, usually one of taking on hordes of monsters. If the monsters kill you, then you can't play. Having a PC die should be a major event, not an everyday occurrence, because it changes the dynamics of the plot.
As for your edit... I don't have my books here, but from memory a critical miss in combat also mean that monsters in range get an attack of oportunity and that you lose the rest of your turn. As far as I know, those are already inside the normal rules. Adding fumble rules only add a small event to all this which force you to react. I see it more like a drop of water in a vase. Yes, that one drop can tip the water off... But again, what can't? In the end it is all a sum which determine the end result and the players can affect the vast majority of those drops already.
No, that's not a rule at all. A critical miss means you automatically miss with your attack. That's it. What you're describing is a critical fumble houserule. If you thought that was in the base rules, than I can understand why you're confused that other people are getting up in arms about critical fumbles, because as you said it's a much smaller step from that viewpoint. But that's not an actual rule, and it really is even worse than just dropping your weapon. I would be hard-pressed to EVER play a melee character in those circumstances.
As for the other questions... Those are already covered in the base rules.
Yes, which speaks to my points above. Enemy crits can kill you, but there are things you can do to mitigate them. If your own fumbles can kill you too, there should be things you can do to mitigate
them, but no one ever includes those.