Drowned Disciple can react to itself when it enters play from your dead pile.
You can trigger Drowned Disciple even if a character from your dead pile enters play under an opponent’s control (House of the Undying, The White Shadows). You cannot trigger it if a character enters play under your control from an opponent’s dead pile.
Max twice per phase (as opposed to “limit”) counts towards all copies of Drowned Disciple, so you can only trigger this particular Reaction ability twice, even if you have multiple copies of Drowned Disciple in play. (See Limits and Maxima. Note that a maximum does not usually appear on cards that remain in play through the resolution of their effect, but it works just the same.)