Ekko, Boy Who Shattered Time

Under the official Radiance ruling, a unit whose death is replaced, for example by Unlicensed Armory or by Mordekaiser, Twice Slain replacing his own death, will not try to kill itself again on a later turn.

Boy Who Shattered Time grants the unit "Kill me at end of turn." The rules treat "at end of turn" and "at the end of this turn" as synonymous, so its trigger condition occurs only during the current turn's Ending Step.^359.3.e.16 When that ability resolves, either replacement causes its kill not to happen.^{370.1.a.1370.1.b} The triggered ability still finishes resolving.^407.5 Its specified time has then passed, so it cannot trigger again on a later turn.^391.2392

No. If it is banished and played again before the ability triggers, the returned card is a new unit without the granted kill ability. Moving from the board to banishment makes the card a new object,¹²⁴ and its temporary modifications, including the granted ability, cease to be tracked.^124.1

A legally timed effect can also banish and replay it after the kill ability is already on the chain. The ability remains on the chain, but "me" refers to its original source, not the returned card, which is a new unit.^{359.3.f.1359.3.f.2407.2407.5}

Ekko, Revolutionary's [Action] ability and Chronobreak can use the first timing window, before the kill ability triggers. Neither can be used in response once the ability is on the chain because neither has [Reaction].^309.1.a By contrast, Temporal Breach can respond to the kill ability if it was played from face down after gaining [Reaction].^811.1.b