In terms of a simple system that stops people going "Apocalypse", fifty battles in one day, I think you're overthinking things.
Rather than having a myriad selection of effects punishing you for aliens, simply have a fatigue stat, updated only at the end of each mission. Every turn the battle drags on for, the fatigue stat is increased by something like 0.5% for beginner, up to around 2.5%/3% in Superhuman, so a three turn maximum small scout battle won't be nearly as harrowing as a forty turn bug hunt through a Cloak base.
Outside of combat, every hour - including those spent resting in your cushy Condor, fatigue decreases by 1%, but take a fatigued unit into combat, and all stats but health will be reduced by the fatigue percentage. For a rookie, 1% off an accuracy of 50 isn't much of a problem, but a highly strung sharpshooter tired of all the fighting will really suffer even with low levels of stress.
To avoid fatigue and to cop out for critical soldiers you didn't notice were simply comatose, simply have the Condor and recovery zones as a "fatigue free" zone, and automatically order occupants in order of fatigue so the freshest are the first into battle, whilst you can leave the "last grey on the map" hunt to expendable rookies whilst your command team sits in the Condor drinking brews.
Finally, increases in medical tech could double fatigue recovery, and for the soldier on the go, medikit stimulants could actually have some use beyond stun recovery by temporarily dropping fatigue by 1 point per application, but similarly adding 1 point extra to fatigue every turn per application as well (Yes, overdosing on coffee is a bad thing that will mess you up).
To prevent "cheating the system" by stimming someone on the very last turn to recover them entirely, on mission completion, everybody, even those who never left the ship, gains one final turn of fatigue.
For normal units and tired units that napped on the Condor the whole time, this has no real effect and is swiftly eliminated by the time they get back from base. For stim-junkies, this could potentially send them into a caffeine coma that lasts for days. Shots are still calculated from total TUs, so beyond a certain amount you just won't be bothered to even shoot anymore.
Since injury recovery is obscenely long anyway, I can't really see the point of introducing fatigue penalties for wounds, so eh.
As for the idea of mental stress, again with the over-complicating; It would probably be far easier just to go by number of berserks and panics rather than simple turns.
Losing a soldier after you just torched fifty aliens using a single round from your IC assault cannon is obviously going to have less of a mental detrimental effect than it does on the person who accidentally killed that soldier, was shot in both legs, landed on by an exploding Cyberdisk and spent the entire battle sobbing in a ball in the corner.
Therefore a simple method for measuring psychological stress is simply to add the same 0.5-2.5% every time the unit panics or goes berserk, which is how the game already remarks on extreme battlefield stresses anyway.
High morale and inherent bravery will support people from mental trauma as a "buffer", making high ranking troops even more vital with all the panicky rookies taking instant morale damage whenever they see an alien (I believe this cheerfully encompasses most of the mentioned ideas).
With this, Twitch the 10 Bravery crybaby is more likely to suffer than Lord High Commander Nightmare von Kicksassalot with his 90 Bravery and collection of alien heads.
For each Panic attack, the percent gained is blue, to the right of this red portions of the bar are added for each berserker rage.
For each 1% of blue bar section, the soldier is 1% more likely to panic than go berserk, and of course, 1% more likely to go berserk with each percent of the red bar - People who spend a lot of time coping for their problems by raging are going to spend more and more time doing it than people who are prone to freezing in terror or running away, and with about 50% advantage of one over the other, such behaviour should be "set", making that person purely a berserker or purely a crybaby until they rest up and relax awhile, get some therapy and so on.
This mental damage, being slower to disperse than physical wear and tear typically would go down 0.5% a day, so in beginner, a one off rookie panic attack would be forgotten about over a nice cup of tea, in Superhuman, two turns of panicked behaviour can easily set the poor rookie up with nightmares for the best part of a week, and they have to fly into mop up an ethereal base soon too. Oh dear oh dear.
As a notable aside, physical fatigue in this model would indeed contribute to mental fatigue, as a 50% fatigued soldier would start out at 50 morale, and as low as 5 bravery, and one who's been forced to every mission and hit 100 fatigue can simply be attributed to having a nervous breakdown (and quite rightly too).
In addition to fatigue moral penalty however, mental damage also contributes itself to morale and bravery - the two mental stats, for a double dose.
So, what would happen if this bar were to reach 100%? It depends.
If the bars are mostly even, then stress induced mood swings might be the effect, simply have a random chance of either panicking or berserking in combat even if morale is high (though wish -100% morale, it takes a lot of officer bonuses to pull that off), but these randomly induced fits don't improve morale but do increase mental stress further - they are simply symptoms, and the battlefield is far from helpful.
If the bar is predominately red, then emotional retardation, paranoia, and uncontrolled fits of rage are in order. The soldier gains morale from any kill they make, friend or foe, loses none from friendly deaths, but gains nothing from allied kills or officer bonuses. In addition, they have a fairly large chance of berserking each turn forfieting their turn to start emptying ammunition at any target nearby and raise their mental stress too, even using grenades if they had them in their hands.
Finally, if the bar is largely blue, then shellshock is the big problem. Explosions, gunfire, enemies, everything gives a good chance of panic, morale losses are huge, and panics cause even more mental damage.
Yes, none of the mental disorders grant any particular advantage, though why they should is beyond me, you're not supposed to be breaking your soldiers' brains.
The only cure for these conditions is simply R&R, X-Corps' already present hospital/psych ward will slowly reduce the mental damage and help work through it.
As should hopefully be apparent, I'd like to restate that fatigue levels are NOT capped at 100. Fatigue and Stress can both climb well above, though stats remain at 0 rather than sink below.
Fatigue: Gain 0.5%-2.5% per mission turn. Lose 0.75%(SH)-1% per hour. All stats are reduced by fatigue percentage whilst in combat. Stimulants can temporarily lower fatigue, but increase the gain of fatigue by just as much.
Stress: Gain 0.5%-2.5% per panic and beserk. Lose 0.25%(SH)-.05 per day. Bravery and Morale are reduced by Stress percentage also. The amount of one type of fit will help determine future hits along with higher stress fits:
So what does everyone think? Sorry it's wordy, but I've kept everything simple, which is how UFO should be, the most technical being a multiple "panic/berserk" bar.
I'm open to suggestions, questions and comments. ^-^