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Attacker / Defender	Man	Sky	Earth	Star	Beast
Man	1.0x	1.1x	0.9x	1.0x	1.0x
Sky	0.9x	1.0x	1.1x	1.0x	1.0x

...

Now for crit star drop rate.

Fairly simple, really.

dropChancePerHit = (baseStarRate + firstCardBonus + (cardStarValue * (1 + cardMod)) + serverRate + starDropMod - enemyStarDropMod + criticalModifier) * overkillModifier + overkillAdd

firstCardBonus = {20% if it's there, 0% otherwise. 0% for NPs}

cardStarValue =

	First	Second	Third
Arts	0%	0%	0%
Buster	10%	15%	20%
Quick	80%	130%	180%

...

More spelunking through the game code.
This time I'll see how much NP you charge from a single hit (remember that attacks may hit more than once).

tl;dr:

WHEN ATTACKING:
NP% per hit = Round Down(Round Down(offensiveNPRate * (firstCardBonus + (cardNpValue * (1 + cardMod))) * enemyServerMod * (1 + npChargeRateMod) * criticalModifier) * overkillModifier)

firstCardBonus = {1 if Arts was first card, 0 otherwise. 0 if it's an NP card} ...

GUESS WHO STARTED LOOKING STRAIGHT INTO THE COMBAT CODE.

Me, of course. I need a place to write down my observations.

tl;dr: It uses a weighed table based on each servant's personal criticalWeight and 3 random cards are given 50, 20 and 20 extra criticalWeight.

FIRST OFF.
There's a concept of 'critical weight'. It's called that because it's used for a weighed table. Tally up all the results and you get 100%, and each value is a fraction of the ...

Defender / Attacker

Base Multiplier

Saber

Archer

Lancer

Rider

Caster

Assassin

Berserker

Shielder

Ruler

Alter-Ego

Avenger

Beast

Saber

1.0x

1.0x

0.5x

2.0x

1.0x

1.0x

1.0x

2.0x

1.0x

0.5x

2.0x

1.0x

1.0x

...