I use an action to kill my own Tokiko as a cost for something. She dies, but as a reaction to her death, I play Hope from Death and overlap someone in the current battle instead. Can I use the reaction on Tokiko to create the samurai card at her location, since she was momentarily not considered to be in play and re-entered play by overlapping another personality?
No. Rules, Card states, Overlay: "(A)n overlaying card is not entering play even if it comes from an out-of-play area(.)"
(I)f she leaves play by dying and is revived more than once on the same turn, can her reaction be used each time because it's being used for the first time after she enters play? Or can the ability only be used once per turn, regardless of whether she has left and re-entered play?
Once.