How does Mageseeker Warden work with Temporal Breach? Due to if a unit is at a battlefield and is then banished with Temporal Breach, but a Mageseeker Warden is at a battlefield, it makes the playing to the battlefield an illegal placement. What happens to the unit that is banished?

It depends whose unit is being breached: if the banished unit's owner is an opponent of the Mageseeker Warden's controller, the unit stays in banishment; if the owner is the Warden's own controller, it replays normally.

Mageseeker Warden only restricts opponents ("opponents can only play units to their base"), and Temporal Breach instructs its owner to play the banished unit back to that same battlefield — not the Breach's caster. So when you breach your own unit at a battlefield while your opponent has Warden out, the "play it back" instruction can't be followed: battlefield placement is a restriction that overrides, so the play fails to finalize and the card returns to banishment (Rule 355.17.b, same reasoning as Rockfall Path — FAQ #11673). You can't redirect it to your base, because the location is fixed at "the same location." If instead you breach the Warden controller's unit, they're unrestricted and it re-enters the battlefield as a new object, causing a Showdown there.

One follow-on: after the unit stays banished, a cleanup runs with no units of yours at that battlefield and you'll lose control of it while the state is Open (Rule 187.4.c). Also note breaching the Warden itself is safe — while it's pending on the chain it isn't at a battlefield, so its restriction isn't active when it's replayed.