Bloodborne: The Board Game

Yes — effects on Stat Cards trigger anytime the card is placed into an Attack Slot, including when used to Dodge; Dodge is just a keyword and does not suppress other effects (Official FAQ p1; Rulebook p19).

The wording means the Ability only resolves at that listed Speed, so if a faster Attack kills the enemy the Ability won’t resolve; if the Ability and the Hunter’s Attack share the same Speed the Ability resolves first as written (Official FAQ p1).

Yes — when a Hunter leaves a space containing Enemies as part of a Move action, those Enemies immediately Pursue the Hunter and each move 1 space following the path the Hunter took (Rulebook p14).

Yes — if you Interact while Enemies occupy your space, flip an Enemy Action card for each Enemy and they Attack immediately before the Interact is completed; you do not get to Attack or Dodge in response to those Attacks (Rulebook p16).

Attacks resolve by Speed with faster Speeds hitting first (Fast > Medium > Slow); if Hunter and Enemy Attacks share the same Speed they are simultaneous and apply damage/effects at the same time, and simultaneous effects can cancel an opposing Attack where applicable (Rulebook pp19–20; effects like Stagger are covered on p21).

No — if you are slain you do not get post-Attack heals; when a Hunter is slain they are immediately sent to the Hunter’s Dream and lose all Blood Echoes (Official FAQ p2; Rulebook pp20, 23).