Generally, damage bonuses apply to all martial attacks* (ranged and melee) unless they specifically state otherwise. The main issue is that most damage bonuses of the same type do not stack with each other. So morale bonuses won't stack with other morale bonuses.
Is there something in the text of two-weapon rend that implies it wouldn't stack with morale bonuses, competence bonuses, sacred bonuses, etc.? I can't think of why it wouldn't.
*Spells and magical attacks are a different animal, but not what you were asking about.
Do damage buffs like Bard stuff and Prayer stack with two weapon rend?
Prayer: "You and each of your allies gain a +1 luck bonus on attack rolls, weapon damage rolls, saves, and skill checks"
Inspire Courage (Su): "An affected ally receives a +1 morale bonus on saving throws against charm and fear effects and a +1 competence bonus on attack and weapon damage rolls."
Prayer is a luck bonus, and Inspire courage is a competence bonus, so both of them will stack on weapon damage rolls.
Two-Weapon Rend (Combat): "If you hit an opponent with both your primary hand and your off-hand weapon, you deal an additional 1d10 points of damage plus 1-1/2 times your Strength modifier. You can only deal this additional damage once each round."
So the question is "Is the extra damage from Two-Weapon rend a weapon damage roll?"
Some might say yes, since it's a damage roll, and it's because of hitting someone with weapons.
Some might say no, since the damage isn't actually coming from a weapon, it's coming from a feat.
While its definitely a grey area, I'd say no. The feat seems pretty clear that 1) it's not weapon damage (otherwise the amount of damage would relate to the weapons involved) and 2) that it's 1d10 + 1.5 Str. Trying to add more to what it says it does is a bit of a stretch.
Ah, I see the issue. Two-weapon rend isn't an attack--just additional damage. It's the equivalent of a rogue's sneak attack damage.
You get the bonus damage from Prayer or Inspire courage on each of the attacks that triggered the two-weapon rend damage, but not on the die roll for two-weapon rend itself.
In the same way, a rogue gets Prayer/Inspire courage bonus on the attack that triggers the sneak attack damage, but not on the die roll for the sneak attack itself.