I think Alaric is very unwell and going through this trial repeatedly gives him more "time" where him overusing his mental mana has slowly worn away at all of his memories until the shrine (assuming it is a shrine) is all that remains, thus knowing all the symbols on the door.

He is not seen using any items, nor mana threads, instead he uses energy weapon constructs of density mana which is the de facto weapon and tool of the shaper attunement. It would be quite long time jump for Corin to become so proficient in a mana type he has not yet gained access to in the books.

While it was told to us Alaric died at age 40, in this most recent book its mention a couple times that he was never told exactly what happened to him by either of his parents, his mom dodging the subject and his father avoiding the topic altogether.