Julia is able to drain Fogg's perpetually-regenerating magical battery of its power by repeatedly making it kill her faster than the Library can recharge it. Although she has lost all of her magic, Julia is still a goddess - Our Lady of the Tree.
Quentin is warned against reminding Enyalius that Ares is the god of war: in Greek mythology, Enyalius was the son of Ares and only the god of soldiers & warriors, but the distinction was later lost and Enyalius became a mere by-name for Ares.
At 8:23 Margo says "... alone's my jam, grenouille." French "grenouille" is English "frog".