The debuffs that get applied, do they last until the next hero phase? I did not see it listed in the spell profile.
They last until the next hero phase. If moved at the start of the round they last until the start of the next round.
and after the first time it is cast and moved, the next rounds it moves in the hero phase because it is a "spell" even though it has already been cast? or it shifts to the move phase?
Moving endless spells after their initial casting is done before the the first turn of the round. After players roll off, the person who goes second gets to move a predatory endless spell first. After that, both players alternate between moving endless spells. All predatory endless spells trigger their damage/effect after they are moved. However, Bound endless spells can only be moved by Seraphon players.