Ambush

No. Ambush only permits playing a unit to a battlefield; it has no effect on your base.

Ambush is shorthand for "I may be played to a battlefield where you control units" and "I have Reaction as long as I'm being played to a battlefield where you control units."^[822.1.b] The permission Ambush grants is strictly limited to battlefields — a base is not a battlefield, so Ambush never makes it a valid destination.^[822.1.c] Playing a unit to your base is already permitted by the default rules for valid locations^[355.2.a] and carries no timing restriction — the distinctive benefit Ambush provides is Reaction, but that only applies when playing to a battlefield.

No. Ambush grants the unit Reaction speed, which determines when it can be played — it does not create a window for opponents to respond before the unit enters.

Units resolve the moment they are finalized without entering the Execute step,^[337.1.c] and finalization does not pass priority.^[337.1.a] The unit enters the board immediately, just as any unit played during an Open State would (see also Can I react to units being played?).

This is a common point of confusion with cards like Kha'Zix, Mutating Horror, which has Ambush and triggers if an enemy unit is alone when he attacks or defends. An opponent cannot play a unit in response to Kha'Zix being placed on the chain in an attempt to break the "alone" condition before he enters.

It depends on whether anything else remains on the chain once the unit enters.

When played onto an empty chain, the unit enters immediately, the chain empties, and the turn returns to a Showdown Open State — focus passes to the next player in turn order.^{[337.1.c.1.a]} This catches many players off guard — you move in to attack, Ambush a unit, and expect to retain focus, but your opponent gets to act first.

When played in response to something already on the chain — such as attack or defend triggers, or a spell — the turn does not return to an Open State after the unit resolves, so focus does not pass.^[346] Priority instead passes to the controller of the newest remaining item on the chain.^[337.1.c.3]