does temporal breach make you lose control of the battlefield? for example if you replay a unit there with an 'on play' ability. can they react to the replay with rengar to make you the attacker?

No — you keep control of the battlefield, and they can't make you the attacker.

Control: When Temporal Breach resolves, the unit is banished and then replayed to the same location, pending on the chain. Control is only lost in a Cleanup while the game is in an Open State and you have no units there (Rule 187.4.c). With Temporal Breach on the chain and the replayed unit still pending, the state is Closed, so no cleanup can take your control — the same reason Arcane Shift on a lone unit doesn't cost you the battlefield. Once the unit finalizes and enters, you have a unit there again.

The Rengar reaction: Playing a unit itself grants no priority window, but the replayed unit's on-play trigger going on the chain does — so they can respond. Rengar, Pouncing can't be played at all, since his ability requires "a battlefield you're attacking" and neither of you is attacking. Rengar, Trophy Hunter can be played (enemy unit is present), but that makes him the attacker, not you: your unit entered a battlefield you control (no Contested applied), so Trophy Hunter's entry is what first applies Contested, designating its controller as the Attacker and you as the Defender (Rule 459.2.b) when combat stages.