Very good questions, that many people will ask themselves. I will answer your questions using the Savage Worlds Deluxe rulebook from 2011 (not SW:EX from 2007), in case it helps anyone:
Tonight in my Savage Worlds (...) game, several of the
bad guys, all Extras, were shot, took damage exceeding their
Toughness, and were put out of the fight--which I believe is
technically Incapacitated.
As someone already said above, exceeding their toughness only makes them shaken. Exceeding their toughness with a raise, or shaking them a second time with a physical wound would incapacitate them and put them out of the game.
These same guys made their Vigor rolls, per the Aftermath section
(...) Does this mean they are considered Shaken and suffering from
Wounds? If they are wounded, how many wounds? What penalty to trait
rolls?
If they pass their Vigor roll in the aftermath of the fight they remain incapacitated (p78), i.e. they are alive but cannot do anything apart from free actions like talking. They cannot even walk unless they succeed on a second Vigor roll ("walking wounded", p78). They must be left in the place or carried away with care.
If they fail the Vigor roll, they are dead (p78). End of story.
If they succeed the Vigor roll with a raise their wounds are only superficial and they are no longer incapacitated (p78). It is assumed that they lost conscience but woke up after the fight, or maybe got a minor injury and shied away from battle (cowards!). In any case, they are perfectly functional ("as new").
Extras do not have wounds: they are either dead, incapacitated, or perfectly fine (p68).
One of them was healed by a PC's Ally. The healing roll was sufficient
to heal one wound. How many wounds does he have now? What penalties?
Is he still Shaken?
If an extra is healed by the Healing skill or the Power, the extra becomes completely functional ("as new"). Extras do not have wounds: they are either dead, incapacitated, or perfectly fine (p68). A success in Healing is enough to heal an incapacitated extra.
If the extra is healed in the middle of a combat (using the Healing power) the extra comes back to life functional (no penalties) but shaken (p114). Also note that before you can use the Healing power on an extra while in combat you must determine whether the extra is dead (Vigor roll, as per the aftermath rules in p78). If the extra is dead, no healing is possible (p114).
If the extra is healed after the combat has finished then they are not shaken (it is assumed that they repeat their Spirit roll every few seconds until they succeed).
Note: You cannot use the Healing skill while in combat. The skill takes 10 minutes per attempt, and the combat is over way before that.
In the fiction, is he still suffering from a bullet wound?
If they passed the Vigor roll and they got cured, it is assumed that the bullet wound was bad but not so bad that it could not be cured. Maybe it was just a scratch on the forehead that covered their face with blood (really messy if it ever happens to you!) but after cleaning and a few stitches they are ready for action.
Lastly, they all got Gut Shot on the Injury table. Does this mean that
in the fiction they are seriously wounded, but somehow able to manage?
In the Savage Worlds Deluxe rulebook it is very clear that only Wild Cards roll on the Injury Table (p68). Extras never roll on the Injury Table according to the rules (but you are free to do it as GM, of course, if it fits your style / story).
Absolutely, Savage Worlds can run that type of game. There's even an official published setting that might do what you need it to...
Its called Deadlands Noir, a Raymond Chandleresque mashup with horror and magic elements, and contains additional rules for various things that you might find in a mystery game, including:
- Detective work (split between Hitting the Books and Legwork)
- Interrogation
- Patter (an extended type of persuasion used to defuse
tense situations)
- Tailing
The default geographic location is New Orleans in the 1930s, and there is a detailed background with districts, individual locations and characters from the city. It's a well supported setting, with a recent companion book that widens its scope to other cities at the time, and there are a number of published adventures.
I've run a couple of mystery based adventures using the setting, where the PCs played Private Investigators, and they went down extremely well.
The only caveat to Deadlands Noir is that it is predictably set in the Deadlands universe, and as such has quite a lot of fluff that you might not want if you want to run a more generic Noir setting. However, it would be pretty straightforward to remove anything you deem unnecessary.
Best Answer
At a convention, playing time is a rare commodity and I generelly recommend not being "that" player who holds everything up with discussions. For the record: I'm from Germany, so my convention experience might differ greatly from yours, all of the following is just my subjective opinion on the matter.
So if what the GM is doing is ruining your fun at a convention game, yet isn't interested in changing anything about that, the main question in my mind is: Does it affect the other players? If they feel the same as you do, I feel it's valid to point out that the way he runs the game isn't fun for the players.
But if they don't seem to mind either, then the path of least resistance is to just get up and leave, be friendly, be polite (the guy wasn't trying to ruin your fun on purpose, after all), try to avoid in-depth discussions on the spot (those tend to get heated and personal quickly and hold up the game for everyone) and just say it's not working out for you. If the GM is honestly interested, offer to talk to him afterwards and calmly explain the matter then.
I generally would only inform convention staff if you feel like the GM was actually trying to ruin the players fun on purpose, I know it can suck if you don't get the game you like, but in my experience, there's a big continuum of styles from "complete freeform" to "everything 100% RAW, all the time, no exceptions", and I don't think it's worth making too big a fuzz about a GM running the game in a different way. Just make it a point to avoid that GM in the future.