In the case where data has been temporarily lost, but it’s just been synchronized again and therefore it’s there (again), should I use ‘it’s all back up’ or ‘it’s all backed up’ ?’
I believe that you may be confused by two different uses of the phrase “back up”. The two are:
1) As a verb phrase it means to copy data from live to off-line storage as a security measure in the case of failure, corruption or data loss. When we schedule the copy we say “We’re going to back up the data”. When the data has been copied we say “It’s all backed up”. When the data has been copied back from backup to live we say “The data has been restored”. Sometimes we say “The system has been restored” but that means that it has been returned to a known, stable condition: it does not, necessarily mean that the system is available for use.
2) As an adjective phrase it refers to the system rather than the data and means that the system has been unavailable but is now available again. In that case we say “It’s all back up.” However we are talking about the system and its availability rather than the data.
When all the data have been written to backup media we say “It’s all backed up”.
When a system has failed but the data can be restored we can say “It’s all right, it’s all backed up”.
When the data has been written from backup to live but the system is not, necessarily, available we say “It’s all been restored”.
When the data has been restored and the system is available we say “It’s all back up”
The phrase and meaning that you need is dependent on the context