Pesachim 117: Praising God Out of Time

On the authorship of the book of Psalms - ascribed here to King David, though that is not a given by any means. Especially given that some of the events mentioned in Psalms predate King David. Yet, some ancient Hallel (which is made from psalms) seems to have existed forever, as it were. So when were these psalms written?! Also, what makes these passages personal to King David and also universal across the generations? And then, to this day, we're supposed to stop and say Hallel, praise to God, the night of the seder. Note - we are to give praise for God's sake, rather than for the sake of human beings. Plus, several historical events throughout Tanakh, at which points Bnei Yisrael said this praise. Also, the mishnah on the third cup of the Seder (at Birkat HaMazon). And the fourth, with Hallel.