What happens if a TX was a double spend? What happens if the 'High' risk option (one confirmation) was chosen and then the TX turns out to be a double spend in the end? Would the value deposited be revoked? Would the user be notified somehow?
The appearance of a double-spend on the network throws the status of the earlier payment into doubt.  The doubt is only resolved when one of the payments is confirmed.  As always, the more confirmations, the more certainty that the payment will be permanent.

The recipient of the payment that was double-spent is NOT notified very quickly.  The bitcoin network itself tries not to propagate double-spends.  Therefore, the earliest that recipient reliably learns of the problem is when the double-spend is actually confirmed in a block.

Even then, most wallets are not very vocal about notification.  This is an area where bitcoin could improve.  A bitcoin core improvement request initiated by Gavin Andresen does exist.