Quark and Odo refer to Rom being an engineering idiot, but later he'll become an engineer for the station and quite talented.
As people started getting the aphasia virus, they were not incapacitated immediately, and they were brought to the sick bay to be monitored. When Sisko got infected, he started babbling, then, started sweating, then collapsed. Soon after that, Kira got infected and started babbling, but she realized what was happening, so she calmly sat there and watched the doctor she had abducted from Bajor as he worked on trying to create the antidote.
The device is said to build the virus directly into the replicated food, however a replicator can't create life which, although simple, a virus is.
O'Brien is the first to contract the virus as he worked on the replication which contained the device, however the device didn't activate until after he ordered his coffee so he shouldn't have been affected.
O'Brien is the first to be affected by the virus and is taken to the temporary emergency sick bay that will be used for all patients. No one contacts his wife to tell her what's happened.
Once it was realized that the virus had mutated to being airborne, why not have everyone wear some form of breathing apparatus? There probably wouldn't be enough for everyone, but more could have been replicated.
When talking to Odo in his vacant bar, Quark refers to Rom as his assistant. It has already been established that Rom is Quark's brother, and Nog, his nephew.