The Takedown action [DH p. 122] and unarmed combat after errata [DH p. 197] give a specified amount of damage for their effects to occur. Do folks run this as raw damage or damage after armour and/or TB reduction?

Secondly, how do you run the Takedown action as listed in the Talents section, is it supposed to be a standalone action or something that is supposed to supplement a Standard Attack?

Finally, since a creature with natural weapons can never be counted as being unarmed presumably that precludes them from causing fatigue from their "unarmed" attacks.

The fatigue point from unarmed combat damage only applies if you inflict at least one point of damage AFTER armour and toughness. Yes, it is much harder to KO someone in power armour with a bare fist! It is likewise harder to inflict a brutally painful blow on a 150kg pile of muscle and bone mass than it is to do the same to a 50kg Schola-runt. This means that your 5 year old sister is statistically much less likely to slap a UFC cagefighter silly than a grizzled Imperial Guard Sergeant standing in for your sister would be. This is a GOOD thing!

Takedown is esentially a modified use of the Standard Attack action. You resolve the attack as normal and then if you manage to score at least one point of damage after soak, then the damage is ignored and the target makes a Toughness test instead to try avoiding a nasty stun.

Critters with Natural Weapons do not inflict the bonus fatigue point, as they are not fighting unarmed. The point behind unarmed attacks bringing some fatigue damage with them was to allow for some non-lethal barroom brawls to break out in your game. Otherwise you would have to put someone into criticals before the fatigue starts to show up, and torn off limbs rather obviously trump a black eye and bruised knuckles on the medicae triage list.