First the links:
Eldritch Reciprocation
You can choose to take extra damage from an arcane spell to replenish mythic power. When you are hit by or fail a saving throw against an arcane spell that deals hit point damage, as an immediate action you can choose to take damage as if that spell were affected by the Maximize Spell feat. If the spell’s damage can’t be increased by the Maximize Spell feat or is already under the effect of the Maximize Spell feat, you instead take double damage from it. The spell’s damage ignores your spell resistance, energy resistance, energy immunities, and other protections against damage.
If you take at least 25 points of damage from the spell, you regain one use of mythic power.
True Archmage
At 10th tier, whenever you cast an arcane spell that targets one or more non-mythic creatures, each of those creatures must roll any saving throws against the spell twice and take the lower result.
You gain spell resistance equal to 15 + your highest arcane caster level, but only against arcane spells. Once per round when your spell resistance protects you from a spell cast by an enemy mythic creature, you regain one use of mythic power.
Divine Vessel
At 10th tier, whenever you cast a spell that targets one or more non-mythic creatures, those creatures must roll twice for any saving throws associated with the spell and take the lower result. Whenever you are healed of hit point damage by a spell or effect, you are healed for the maximum possible amount. You also gain DR 10/epic. Once per round when you take more than 20 points of damage (after damage reduction is applied), you regain one use of mythic power.
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Question 1) Can the character cause injury to themselves, or have a companion do so, in order to make use of the powers?^1
Question 2) In the case of Eldritch Reciprocation, does the recipient of damage know how much damage they are going to take, before activating the power? (How much it would result in)^2
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^1 - The possible abuse: a T6 or T10 Archmage or T10 Hierophant can recover all Mythic Points out of combat (via Snowball (CL 5+ for Eldritch Reciprocation, CL 1 for True Archmage), someone in the party hitting the Hierophant for 20+ damage.)
^2 - In order to choose whether or not to use the power, would the Archmage know the difference between a normal CL 1 Magic Missile spell (taking 4-10 damage) and a Mythic, Augmented, Maximized, Intensified, Arcane Channeled Magic Missile ((Max(2d4+1))*((5 Missiles+2)*2)*1.5=9*14*1.5= 378 damage!) Feel free to address those Metamagic and Mythic abilities on a case by case basis.