Sorry did not address your first question. Well lets assume that enchanted items and the templars will eventually lose power, which we have no evidence either way. There is 2 explanations for this. The scientific one is that mages consume a lot more power than items or Templar powers. Then there is the other one...magic. Because it is magic it can work one way for one situation and work in a completely different way for another. Hence why it is important to focus on what is actually stated in the game rather than drawing our own conclusions.
Nah, I'm not taking this:
for an explanation.
The way templar abilities and enchantment are presented in game, it is magic, and there is no difference between mage spirit school and templar abilities, or enchantment and mage weapon infusion.
Mages need fuel for their abilities and that fuel runs out, so it should be no different for enchantment and abilities granted by lyrium.
If you have no logical explanation as to why these should be different, and you are going to say: ''It just is.'' and ''It's irrelevant why.'' Then there is nothing to discuss.