Empower

Yes. Empower is an activated ability keyword,^[827.1] and activated abilities use the chain.^[377.3] After the ability is finalized, opponents have an opportunity to react before it resolves.^[377.3.b.2]

This differs from activated abilities that use Add, which resolve immediately when finalized and cannot be reacted to.^{[337.2][429.2]} See also Can I react to triggered and activated abilities?.

By default, only during your own Main Phase while the turn is in a neutral open state.

An Empower ability is an activated ability,^[827.1] and activated abilities can normally be activated only on their controller's turn during an open state.^[381] Because Empower has neither Action nor Reaction by default, it cannot be activated during a showdown or in response to another chain item.^{[308.1.a][309.1.a]}

An Empower ability may have text that changes its timing.^[827.1.c.4] If it explicitly has Action or Reaction, follow the permissions of that keyword instead.

No. If the unit is killed, returned to hand, or otherwise leaves the board before its Empower ability resolves, it does not become Empowered and its "When I become Empowered" ability does not trigger.

The Empower ability remains on the chain, but the Empowered state exists only for game objects on the board.^[441.2] Because triggered abilities of permanents can evaluate their conditions only while their source is on the board, its dependent "When I become Empowered" ability is not active and does not trigger.^{[384.2][828.1.c][828.1.d]}

Yes, if a game effect instructs a player to empower it.

The Empowered state can apply to game objects on the board; it is not restricted to cards with printed Empower or Empowered abilities.^{[441.1][441.2]} Players cannot empower a game object at will, however; they may do so only when directed by a game effect.^{[441.3][441.3.a]}