Alberich mana mechanic

Yes, that is correct. The mana gain increased buff (from Ariel, Khagan, etc) is affected by the amount of mana gained by the defence through getting hit by tiles and over turns.

Yes, heal over time buffs HPRecovery are affected by the healing bonus from troops.

The healing bonus acts like Tritons healing up buff RecoverUp and also stacks with it. Ditto the healing bonus node from Class trees.