What is the damage return type of blademail? Does it matches the type of the damage source or has a fixed damage type(chaos,hero, magical or pure)?
The damage returned is pure type. The amount of damage applied is the same as the enemy hero actually took.
As of patch 6.87, magic immunity no longer blocks the returned damage from Blademail. Also the damage returned is applied before any damage reduction, and matches the damage source. Physical damage will be returned as physical, magic as magic, and pure as pure.
From the Dota2 Wiki
The damage return is Pure.
The amount of damage returned is what you received after armor and magic resistance is calculated.