Another mistake, and he will be fired.
Are we missing a verb here? The German sentence looks incomplete to me.
Er wird gefeuert werden = He will get fired (This is what I would expect)
Er wird gefeuert sein = He will be fired (“He will be in the state of having been fired”, this one is maybe a bit weird)
Er wird gefeuert = He gets fired (?)
Yes! This is regular present tense passive.
“Er wird gefeuert werden” is the future passive. This also works but feels unnecessarily verbose.
German uses future tense less than english, and we can say “Ich gehe morgen ins Kino”, and use present tense when time indicators or the context make it clear what is meant.
“Ich werde morgen ins Kino gehen” sounds kind of unnatural unless you want to emphasize it somehow, e.g. it sounds like “… and you’re not going to stop me”.
Okay, that makes sense. Interestingly, all three options also work in English, though the future tense certainly sounds the most natural to me:
One more mistake, and he will be fired!
One more mistake, and he’s fired!
One more mistake, and he gets fired!
Ok, this is just my “Sprachgefühl”, but I feel there are tendencies towards certain situations and speakers:
… und er wird gefeuert
… und er ist gefeuert
This is something the boss would say, as a threat (with “wird”), or matter-of-fact statement (“ist”), or as an order to others to fire him in case he makes another mistake (also “wird”).
The latter is because passive is also used for commands in a matter-of-fact or that’s-the-rule style:
Jetzt wird gegessen! - Now we’ll eat!
Hier wird nicht rumgerannt! - No running around here!
Hier wird ordentlich gearbeitet! - Work is done properly here!
… und er wird (noch) gefeuert werden
This might be used when friends of the poor fella express their worries. It feels like “and he’ll end up getting fired” or “and they’ll fire him”.
… und er wird gefeuert sein
You are right, this is the least useful form. The only application that comes to mind, is when you list the steps on how to fire someone:
Man macht zuerst Schritte A, B und C. Dann macht man noch Schritt D, und er wird gefeuert sein (or ist gefeuert).
Basically this form implies/needs some event after which he will have completed the transition to a state of having been fired.
It is of course very unlikely that such a situation comes up where you would want to say something like that 