First one is a bit difficult as we don't have the mechanical analogy. What I'd do is have Harry declare how much magical energy he's going to use in advance. I.e. he declares "I am going to use all my mental stress boxes, my mild consequences and my moderate consequence". This has the following effects;
a) In that scene, once he uses up everything he declared he would use, he no longer has any energy. I.e. he can't use his serious consequence by pushing himself - there's no more energy to channel.
b) Once the scene ends, if he has declared mental stress he did not use during the fight, those consequences/stress boxes are still filled up. He had used them to summon up that much magical power - he had just been holding it inside unused during the fight but he can no longer hold it.
Second is very easy. Mechanically, Harry asked Lara to use her Incite Emotion on him to apply aspects - one of the standard uses of that Power. Then he tagged those aspects, increasing his spellcasting rolls. It would be the same thing if Lara had applied those aspects on a soldier fighting for her and then the soldier tagging the aspects to boost his combat effectiveness due to improved morale and/or willingness to fight.