In game you do it at the screen where you select your character and equipment - the ability descriptions are listed where it says level 1 2 3 and 4. The reason for this is because in "Non Codex Mode" you don't start with all abilities unlocked - and instead unlock them as you play.
However for quick reference here:
(I did not make that guide)
Thanks for the shout-out
Both Protector (Tactical) and Energy Field (Assault) have descriptions under their respective Levels that say they each should last for 10 seconds, however after 5 seconds the visual effects disappear and the skills both go on cooldown. It appears they are each lasting for only half of their intended durations.
Axe Specialist and Sword Specialist are both kinda pointless when Battle Psyker is a thing. Why take 25% increased attack speed when you can have flat 30% damage increase. In terms of DPS, 30% additional damage over time is greater than 25% additional damage over time.
Additionally, why ever take the Force Sword over the Force Axe? The strength of the Librarian is in his casting abilities, and thus you want the cooldowns on his skills to be as low as possible. The only possible way I'd see Force Sword ever being taken is if it received a large buff to damage or attack speed, to the point where it is greatly a better choice than the Force Axe in terms of melee attacking. As an aside to this, I think Redemption should allow the use of Force Sword and Force Axe for Librarians and Crozius Arcanum for Interrogator-Chaplains. No real sense in restricting those two classes to Power Fist when using the Redemption.
Finally, multiplayer has different skill cooldowns and cooldown reductions on all the Librarian's abilities compared to singleplayer Campaign and singleplayer Special Missions when using the Force Sword or Force Axe. From my calculations, Force Sword has a 25% cooldown reduction while Force Axe has a 37.5% cooldown reduction (in multiplayer). However, Force Axe seems to be bugged in this regard when modifying Spontaneous Combustion's cooldown, which goes from a 90 second cooldown (base) to 67 second cooldown (Force Sword, 25% reduction) to 45 second cooldown (Force Axe, 50% reduction). I would expect Force Axe to reduce Spontaneous Combustion to ~56 seconds instead of 45 seconds. Thus, Force Axe is even stronger than it should be compared to Force Sword.
Same complaint as the OP, but in terms of the Redemption, which is currently locked to Power Fist on the Chaplain and Librarian. Really sad, since it is a cool weapon but not worth taking over a Storm Bolter when you lose out on the Crozius or Force weapons.