I can answer your second question for him if you care to read:

First i'll start with it's Similarities:
The first key thing you obtain from either Item is the Burst of Movement Speed(As you know, Phage has a unique passive that doesn't double on itself twice). This makes it so that half of the Black Cleaver would be useless along with 1/3rd of Trinity Force. They also give Cooldown Reduction which is Great on Darius.

Now for their Key Differences & why or when to pick one and not the other/or grab both:

Unlike Trinity Force, Black Cleaver reduces their Armor for every hit you land on the target you are focusing down. This will allow a higher percentage of the damage mitigated by their Defenses to penetrate dealing your full Damage on Your Auto Attack or Abilities. Black Cleaver is the item that pushes your damage to almost being True Damage.

Trinity Force on the other hand Increases the damage by giving you more Utility. It gives you the movement speed like Black Cleaver, Cooldown Reduction(Like the Cleaver), grants a Bonus % Movement Speed, Grants higher Attack Speed, & Give you the Sheen Proc.

Essentially they both do the same thing by increasing Darius's Damage & the way Trinity Force's Stats sound make it seem like a better choice, right? Well, let me ask you this: What do you think happens when you Lower their Armor with Black Cleaver?

The answer is that you & your important Carry's( Caitlyn, Talon, etc) will be dealing their fullest damage to the Target.

Trinity Force is more of a Personal Item with a very high Cost which is why it's only bought when you're Drastically Ahead(Not to mention if you're against a Super Tank you won't be doing damage to them without 5 stacks).

These two items together are absolutely Cheese on Darius but if you're behind in any way, you will find yourself greatly agitated trying to gather up enough gold to purchase both Items & still be able to build the essential Defensive items to follow the Mid-Late Game.

Conclusively, Although Trinity Force provides the greatest Utility & Objectively Fun Stats, Black Cleaver outshines on this choice with it's Conveniently low cost & Tank Buster Stats. Buying these two in the same Build are NOT recommended unless you are strictly Ahead Period.

I hope this shined some light on your question!

Fun Side Note: We call the Trinity Force on Darius "The Squishy Slayer".