@Scott
Notice that there the "Occurrence History" shows 7 engine starts and 1 smoke detection before the final flight.
"02-ENG START" labelled ACARS is refering to the flight phase (06 is Cruise) ; those ACARS, like "FWC2: no data... ; QAR Media low..." are triggered only when such circumstance apply, but not each time an engine is started. It looks like the "occurence history" is covering a period of previous flights for each ACARS.
Flight Warning "SMOKE LAVATORY SMOKE" appears to have been previously triggered once, but when was that? If each box, starting from the last one, was for a previous flight, I can count 15 boxes (including the last flight) and going backward, it would have been 8 flights before the last one.
On the other hand, I can't see any occurence history for "AVIONICS SMOKE" during the past 14 flights (if that's how it works). We can't say anything about "CARGO SMOKE" history, because it's not been triggered during the last sequence, neither about "AIR COND SMOKE" which is not triggering any ECAM warning.
Consequently, without any specific ACARS reports from those previous flights, this isn't going to be really helpful. I would only deduct that "SMOKE LAVATORY SMOKE" or "AVIONICS SMOKE" were probably
NOT triggered during the previous
24h of operation.