Original perks alphabetically ordered, updates below originals

(AbilityName="F_Adrenaline")
(AbilityName="F_Ambush", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_AmmoConservation")
(AbilityName="F_Avenger", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_Blend")
(AbilityName="F_BlindingFire", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_Bloodlet")
(AbilityName="F_BolsteredWall")
(AbilityName="F_Botnet")
(AbilityName="F_CallForFire")
(AbilityName="F_ChipAway", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_ColdBlooded")
(AbilityName="F_ControlledFire")
(AbilityName="F_CombatDrugs")
(AbilityName="F_Compensation")
(AbilityName="F_Concentration")
(AbilityName="F_Corpsman")
(AbilityName="F_CoverArea")
(AbilityName="F_Dedication")
(AbilityName="F_DisablingShot", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_FaultlessDefense")
(AbilityName="F_FieldMedic")
(AbilityName="F_Finesse")
(AbilityName="F_FireFirst", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon) (AbilityName="F_FireFirst", ApplyToWeaponSlot=eInvSlot_SecondaryWeapon)
(AbilityName="F_FirstStrike", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_Flatline", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_Havoc", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_Immunize", ApplyToWeaponSlot=eInvSlot_SecondaryWeapon)
(AbilityName="F_Imposition")
(AbilityName="F_KillEmAll", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_LickYourWounds")
(AbilityName="F_LikeLightning", ApplyToWeaponSlot=eInvSlot_SecondaryWeapon)
(AbilityName="F_LockNLoad", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_Maim", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_Momentum", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_OpenFire")
(AbilityName="F_Opportunist")
(AbilityName="F_PierceTheVeil", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_Predator")
(AbilityName="F_Preservation")
(AbilityName="F_ProtectAndServe")
(AbilityName="F_QuickFeet")
(AbilityName="F_QuickPatch")
(AbilityName="F_Rally")
(AbilityName="F_ReadyForAnything", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_Recharge", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_RegenerativeMist")
(AbilityName="F_Renewal")
(AbilityName="F_Resupply", ApplyToWeaponSlot=eInvSlot_SecondaryWeapon)
(AbilityName="F_Rush", ApplyToWeaponSlot=eInvSlot_SecondaryWeapon)
(AbilityName="F_SaltInTheWound")
(AbilityName="F_ShieldTrauma", ApplyToWeaponSlot=eInvSlot_SecondaryWeapon)
(AbilityName="F_ShoulderToLeanOn")
(AbilityName="F_SniperElite")
(AbilityName="F_StationaryThreat", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_Steadfast")
(AbilityName="F_Stiletto", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_Stimulate")
(AbilityName="F_SurgicalPrecision")
(AbilityName="F_Survivor")
(AbilityName="F_TheBiggerTheyAre")
(AbilityName="F_ThousandsToGo", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_TrenchWarfare")
(AbilityName="F_Triage")
(AbilityName="F_Unload", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_WarningShot", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_WatchThemRun", ApplyToWeaponSlot=eInvSlot_PrimaryWeapon)
(AbilityName="F_WellProtected")
___________________________added from May 2019 update___________
(AbilityName="F_CalmMind")
(AbilityName="F_Indomitable")
(AbilityName="F_PerfectGuard")
(AbilityName="F_ShieldRegeneration")
(AbilityName="F_StayCovered")

FireFirst can be used on both primary and secondary weapons AFAIK. I believe the correct animation for each weapon type is picked up in the game.

Note - I haven't tested all these abilities, either on their own, or working with others in a full set. As you appreciate there are a lot of combinations. So use with the DEBUG on any soldier class you have and check it works before starting a campaign you care about.

This looks like what I'm looking for. I'm trying to add some of these to the general XCOM perk list for the training center using the I'm the Commander Here Extension configs, which has as an example of the syntax:
So to get this to work for, say, Stiletto, should I do:
?

I believe the way that mod works is by looking at a soldier class that has already been defined. The Config folder has the XComImTheCommanderHere.ini file in it and shows how it links to the soldier classes that are built for the RPGO mod.

If you want to add Favids abilities to the vanilla classes then they need to be added into the game with the AWC picking them up. The only way I can think of doing that without making a mod is to create a RandomAbilityDeck of all the abilities you want, then add it to your XComClassData.ini between the Rookie and Ranger template. Hopefully the game would read this and add them to the game but I've never tried doing it that way to say for certain.

Check my guide if you're not certain of how to create a RandomAbilityDeck.

PS - the AWC is the internal game mechanic for placing random abilities even in WotC and I'm not certain if I'm The Commander Here reads from the AWC or all soldier classes. If I can think of a better way I'll let you know, but please post an update of what happened for others to learn from.

Well, I may as well document what I've done. In the XcomImTheCommanderHere.ini file for the I'm The Commander Here Extension config, I tried doing the following with several perks:
This caused them to show up in an ongoing campaign; I could use the Respec feature from I'm The Commander Here to reassign them to my soldiers' XCOM abilities from the AWC, and they showed up on the randomly-assigned XCOM abilities of newly-received soldiers. They had appropriate text and icons, and for Ammo Conservation when I tried it in a mission it even had a button in the tactical mode which could be clicked…it just didn't actually do anything (nor did having Stiletto on my Sharpshooter cause her to pierce any armor).

After reading this and your guide, I tried using the format:
but that caused them not to show up at all. (Though weirdly, the Stiletto unlocked on my Sharpshooter was still around and still had appropriate text).

Interestingly, I tested Rainmaker, which was the template ability in the .ini file, and it didn't work either; the rocket launcher still had the same radius and damage as the rocket launcher of the SPARK without it. So maybe it's the UnlockAbilityAsCrossClass thing in I'm The Commander Here that isn't properly integrating the abilities somehow?

So, I thought I'd add Renewal into my random XCOM skills pool since it isn't tied to a weapon, tried it on a mission, and discovered it reliably crashed the game any time I ended a turn with a soldier wounded. Healing the wounded soldier back to full before ending the turn allowed it to proceed. It's entirely possible this is from a conflict with one of the many other mods I'm using, but I figured I'd mention it anyway.

To add to my first response on creating a general XCom ability list...

In the XComClassData.ini at the very start is a template called [XComGame.X2SoldierClassTemplateManager]

My understanding is that this adds abilities described in another soldiers ability deck to the AWC for random selection. In a non modded file it adds LighteningReflexes from the Skirmisher class for other classes. As you scroll down you then find that Rangers and Sharpshooters have this excluded so they don't have a conflict with ShadowStep.

If you add a RandomAbilityDeck into file, giving it a name, adding all the abilities you want, but not using the deck for any soldier; you will have effectively loaded all those abilities into the game. Using the above template you can then copy over the "Friendly Name" of those abilities and follow the example for LighteningReflexes to have them called upon in a random fashion.

*Remember - you will still need to have subscribed to a mod that has the ability you want to use.
**Double check the ability works as you hope it should.

THANK YOU!!

@initium Thank you so much for this!

It‘s cool