How did Christians in Imperial Pagan Rome practice Christianity during the persecution while serving as the emperors?
I think you mean 'serving the Emperors'. I think the "Miracle of the Kolyva" is instructive. Destro knows what I'm talking about.
The Orthodox have a commemoration "Theodore Saturday" which commemorates an event whose name strikes Westerners who have imbibed too much Thomism as bizarre. The Miracle of the Kolyva was a sign of God's presence and care for the Church, which did not involve the overthrow of any natural order, but simply a good intelligence report: one of the pagan emperors wanted to disturb the Christian's fasting, and ordered that blood from the pagan sacrifices be sprinkled on all the produce in the markets. The plan to trick the Christians into breaking their fast and (worse in some minds, irrelevant in others) partake of food offered to idols was foiled because St. Theodore who served in the Emperor's bodyguard was a secret Christian, and passed the word of the plot to the local bishop with the suggestion that Christians eat only kolyva--boiled whole grain wheat--from Christian
farmers fields.
There were plenty of secret Christians during the Roman persecution, and plenty during the Bolshevik, just as there were plenty of martyrs under both (indeed more under the Bolsheviks).