"Amazoness Swordswoman" only applies her effect to Battle Damage to her controller, so if attacked by a stronger monster, the "Amazoness Swordswoman" herself is still destroyed as normal.
Damage inflicted to the opponent when "Amazoness Swordswoman"'s effect is activated is Battle Damage, so the opponent cannot use "Barrel Behind the Door".
When "Dark Ruler Ha Des" attacks "Amazoness Swordswoman", the effect of "Amazoness Swordswoman" is still resolved.
When a monster affected by "Diffusion Wave-Motion" attacks "Amazoness Swordswoman", the "Amazoness Swordswoman"'s effect is applied and the opponent (who used "Diffusion Wave-Motion") takes the damage dealt to Life Points. Likewise, the controller of "Spear Dragon" takes damages when "Spear Dragon" battles "Amazoness Swordswoman" (or the controller of a monster equipped with "Fairy Meteor Crush", or who used "Meteorain").
When the controller of "Amazoness Swordswoman" uses "Kuriboh", the controller takes zero Battle Damage so no damage is dealt to the opponent.
When "Susa Soldier" battles "Amazoness Swordswoman", the controller of "Susa Soldier" takes full damage; the damage is NOT halved.