The 787 when cleared to fly will have a backup source for the brakes as the new battery and it's associated systems will have been certified as being safe and reliable.
Certified as safe: Yes. Certified as reliable: Highly unlikely.
The fireproof box and containment system appears to based on solid and proven engineering priciples, however will need to demonstrate its ability to contain the same failure scenario as on the ANA flight before it will be certified.
There are two ways to demonstrate reliability: The first is to deterministically ascertain and then eliminate the root cause of whatever caused the device to not meet the previous reliabilty certification criteria (i.e. 1 fire in 10 million hours).
The second way is to create a new device with moderate reliability claims based on engineering design, then to demonstrate higher reliability through accumulated service hours without incident.
The first method CANNOT yet be applied to the 787 battery as the root cause has not yet been determined. Most aspects of the new design such a separated/insulated individual battery cells, are containment improvements to offer better protection in the case of failure - they do not reduce the risk of the failure and thus do not increase reliability. Production changes such as tighter tolerances may help reliability, but there is no way of knowing without a deterministic confirmation of what the root cause failure mode is.
The 2nd method is what is commonly used for ETOPS certification. A new model aircraft/engine will typically have a moderate ETOPS rating based on the number of incident free test hours during certification. A case can then be made to increase the duration of the ETOPS certification as the number of incident free hours increases.
The problem for Boeing is that they don't have the luxury of time to go through thousands of hours of inflight testing of the "new" battery to demonstrate reliabilty using this method.
As such, I would expect the 787 to resume flights with a reduced ETOPS limit and stricter MEL (e.g. APU must be functional) until the reliability (or otherwise) of the "new" battery solution can be proven. I wouldn't be surprised to see additional operational requirements such as having the APU ON during takeoff, approaches and landings.