Let's suppose some enemy of Rome spent some weeks slowly infiltrating soldiers as roman citizens. All the attacks starts from the very heart of the most important places and spreading. They start a killing spree not caring if they are soldiers or civils, adults or kids.
Goverment:
Military:
Society:
In case of victory, what would have been the steps taken to restore the order and rebuilding?
In case of defeat, and based on the behaviour of that era: the enemy would have taken control of Rome or they would destroy and burn the city?
Thanks for your answers and sorry if there's any mistake, english is not my native language.
Just one thing to help in answering....
What period of time are you taking about?
Let's suppose some enemy of Rome spent some weeks slowly infiltrating soldiers as roman citizens. All the attacks starts from the very heart of the most important places and spreading.
That's so unrealistic it hardly qualifies as what-if history. It would require so many men that it'd be better to just form an army and march to Rome and it would be impossible to organise something on such a scale across such a geographic area. Keeping it a secret with that many people involved would be even more impossible. And how would these infiltrators get the equipment to murder all those people? The mob is going to have access to whatever equipment the infiltrators will have access to.
I guess what comes closest to what you're describing would be the Third Servile War, which started as a small slave revolt and escalated into a full-blown war with Spartacus leading the former slaves. The escaped slaves plundered the countryside, encouraging other slaves to join them. The success of the revolt meant that Spartacus' following grew to over 100000 men, women and children.
So how did the Romans respond? In this case, the Romans sent a praetor with a small militia army to quell the uprising. The army was defeated, so the Romans sent another praetor with a slightly larger militia army. That army too was defeated, so the Romans sent both consuls with their full armies. Those armies were defeated, so the Romans sent an even larger army under the command of one of their best generals, Crassus. That army was as large as the Roman army which fought Hannibal at Cannae. This finally settled the matter in favour of the Romans, but just in case it wouldn't, a reinforcement army led by Pompey was on its way. It arrived just in time to do some mopping up.
Having mentioned Cannae, it might be interesting to know that for a bit during the Second Punic War (after Cannae), the Romans nearly ran out of soldiers to throw at Hannibal. So in an exceptional event they armed prisoners and slaves and threw those at Hannibal.
Now all of this happened a few centuries before the time you're asking about, but the basic Roman attitude was still the same at the time: throw soldiers at the problem. If that doesn't fix it, throw more soldiers at the problem.