Temporal Breach

No, when Temporal Breach is played from Hidden, the unit it banishes must be chosen from among units at the battlefield where it was hidden.

"Banish a unit" chooses a specific game object to affect, making it a target, declared as Temporal Breach is put on the chain.^{[355.5][355.7][355.8]} Choices made while playing a card from Hidden are restricted to the battlefield where it was hidden.^[811.1.d] Specifically, if a Hidden spell chooses any targets, those targets must be chosen from among options at that battlefield, unless the ability explicitly restricts targeting in a way that makes this impossible.^[811.1.d.2] Temporal Breach's own wording doesn't restrict its target to a location, so this Hidden restriction applies in full — a unit at another battlefield, or in base, isn't a legal target when it's played from Hidden.

If Temporal Breach is instead played normally — paying its cost rather than from its facedown state — none of this applies, and it can target any unit anywhere with no restrictions on targeting.^[811.3]

Yes, control of the battlefield is never lost during this sequence.

When Temporal Breach resolves, the replayed unit is added to the chain as a pending item,^[354.2] with its play process held until the spell has fully resolved.^[354.3] Once the spell finishes resolving, a cleanup runs — but the pending unit keeps the chain alive throughout it. Because the chain is not empty, the turn remains in a closed state, and cleanup step 4 — which would make the battlefield uncontrolled — only applies during an open state.^[323.6] Control is never lost, so any effects that care about gaining or losing control of that battlefield don't trigger. When all outstanding tasks are complete, the pending unit is finalized^[335.2] and replayed to the same battlefield you still control, as dictated by Temporal Breach's own text.

Temporal Breach still resolves fully — the banish itself happens normally — but the replayed unit never actually makes it back onto the board. Temporal Breach's own text sends the unit back to that same battlefield with no alternative, and since Rockfall Path reads "Units can't be played here," that replay attempt is illegal; it gets undone during its own finalization, and the unit simply remains in its owner's banishment for the rest of the game.

"Then its owner plays it to the same location" only adds the unit to the chain as a pending item — it doesn't check whether the destination is legal, so Temporal Breach's own resolution is unaffected by Rockfall Path's restriction.^[354.2] The unit only runs into trouble once it's finalized on its own, since checking legality at that point catches units being played to a battlefield where that's forbidden.^[358.2] Because Temporal Breach doesn't offer any alternative destination, that check can never pass, so the finalization attempt is undone and the unit returns to the banishment it was played from^[358.4] — for good.

The step-by-step below spells this out.

The token stops existing the moment it's banished, so there's nothing left for its owner to replay.

Banishing places the token directly into its owner's banishment,^[427.2] which is a non-board zone.^[056.1] Tokens can only exist on the board or the chain — if a token ends up in any other zone, it ceases to exist immediately upon arriving there.^[183][183.1] So by the time Temporal Breach's "then its owner plays it to the same location" instruction would apply, the token is already gone, and that part of the spell does nothing for it.^[055]

Yes, since the replayed unit still goes through the complete, normal process of playing a card, and "ignoring its cost" only narrows one part of that process — the base cost — leaving everything else, including optional additional costs, unaffected.

"Its owner plays it" instructs the normal process of playing a card — the unit is removed from banishment and put onto the chain as a pending item,^[354][354.2] it isn't placed directly onto the board. That pending item goes through the full finalization process once it's ready to be finalized, including making relevant choices^[355] and determining total cost.^[356] Playing a card "ignoring its cost" only sets its base Energy and base Power cost to zero;^[356.1.b.1] further additional costs applied in later steps can still raise the total cost back above zero.^[356.1.b.3] Accelerate is one such optional additional cost, paid as a player plays the unit with the ability,^[805.2] so its owner may still declare their intent to pay it during finalization^[356.2.b.1] and pay it as usual, unaffected by Temporal Breach ignoring the unit's base cost.