[Karinya]

I am not sure if Evasion checks before or after parrying, but they are right next to each other, yes.

This is theoretically testable, but I think the only thing it would really matter for would be skilling up parry. (You'd want to avoid +eva if it stops you from checking parry, the same way monks want to avoid +eva when they skillup guard.)
Speaking of monks, I forgot Counter, which also prevents the hit. Does it go before or after shadows?

I am not sure whether Guard checks before or after shielding, but they are right next to each other as well, correct.

I don't think it's possible for it to ever matter which comes first, since they can never apply at the same time (you'd have to be using a HTH weapon and a shield). Unless you can guard with no main hand weapon and a shield, which I don't think I've ever tried.

Invincible comes after Phalanx (and before Stoneskin),

How could you possibly know that? (Not accusing you of lying or anything, just wondering.) The latter you could determine by seeing that your stoneskin doesn't weaken or wear off during invincible (when taking only physical attacks), but the former?

and TP calculation comes before Phalanx - you can get TP from a hit that would've done more than 0 if you didn't have Phalanx on.

Cool, I didn't know that. I usually combine it with stoneskin, which of course makes this go away, because as you point out

You can't get TP through Invincible or Stoneskin though.

A shame when it happens to you, but nice when it happens to trolls. It means they have to take some actual hits before they have the TP to reapply it.

I'm not positive, but I think that when you shield block a hit that is reduced to 0 later in the series, you don't get the Shield Mastery TP either. (Except for the Phalanx exception, I guess.)

Also, Sentinel and % Damage reduction are separate, but since they're multiplicative it doesn't really matter which comes first and which comes second.

True.