http://yugioh.wikia.com/wiki/Counter_Trap_Card
- Quote :
- Counter Trap Cards can be activated in the Damage Step even if their effects do not alter ATK/DEF.
Both your scenarios are special though, and reasons for not being able to activate, as well as being able to activate, have nothing to do with the damage step.
You CANNOT War Chariot a Jain's effect to increase her attack, as this counts as a Continuous effect, rather than a Trigger effect, contrary to many beliefs. You CAN however, War Chariot the end phase mill.
You CAN War Chariot an Airknight Parshath'S effect to draw after inflicting damage,
EVEN IF YOU DO NOT CONTROL ANOTHER GB MONSTER. The monster will be considered marked for destruction after damage calculation, which removes it's continuous effects, but yet it is still considered on the field at the point where you take damage, and Airknight Parshath triggers.
This issue was addressed a while back by Akira in his blog.
http://duelistcodex.wordpress.com/2008/12/28/gladiator-beast-war-chariot/