I play Temporal Breach to a unit at a battlefield a hidden card. If they don't react it now, will the hidden card get discarded or can they play it later after the unit is played again and will they score this turn? This is my turn.

No — the hidden card stays, and the Breach replay doesn't score.

Your control of that battlefield is never lost during the sequence. While Temporal Breach is on the chain (Closed State), no loss-of-control check happens, and after it resolves your unit is pending on the chain being played back — a pending unit prevents the cleanup from stripping your control (187.4.c, 2026-04-29 FAQ clarification). Since you never lose control, the hidden card is not trashed, and there's no window where it gets discarded. FAQ #11796 confirms this exact line.

The hidden card can be played later as normal — just remember it can't be played the same turn it was hidden (811.1.b); if you hid it on a previous turn, it's available whenever you have priority to play it.

Scoring: replaying the unit does not trigger a Conquer — you never lost and regained control, so no Contested status, no Showdown, no score from the Breach itself. If you already scored that battlefield this turn (e.g., via Hold at your Scoring Step), the once-per-battlefield-per-turn limit means you get nothing more (Rule 470). If you haven't scored it yet this turn, you can still Hold it normally at your Scoring Step.