Were there any events that restructured the praetorian guard? Why did they allow an emperor to rule them? What was their role after the death of Julius Caesar?
Just some questions I thought of but I want to know as much as I can.
I'm slightly confused by your question, are you asking about strictly the praetorian guard, are about the soldiers of the army in general?
The Roman army has always been a force to be reckoned with in the history of the Republic and Empire.
One of the first things an aspiring ruler (be it a consul or emperor) always did, was seek the approval of the army because he knew that without this support any attempt would be useless. A lot of emperors grew up in the army (eg. Caligula) or had a function in the army prior to ascent (best example is the period of Barracks emperors).
**The army also didn't mind stepping in when needed (eg. several assassinations were committed by the Praetorian guards or army) if they thought that it would benefit the people/the army. **
Going back to the rise of Caesar, there are some important ingredients here to take into account:
Loyalty of an army. The loyalty of a Roman army to their general, but also the loyalty of the army to the Roman populace.
the state of the Roman Republic
While the Roman republic was in decline and corruption was frequent, Caesar was succesful as a general and inspired firm loyalty in his army. When he took up the gauntlet to take on Rome and impose himself as ruler, he did this with their backing. He was the man that promised to rid the Senate of corruption and to restore Rome to its former glory. During his rule Caesar gained the support of the majority of the Roman populace what reaffirmed the support of the army for his rule (even if it did imply that he slowely became sole ruler). After the assassination it was clear that the Roman people sided against the Senate and, while some armies supported one or more of the Senators, the majority of the generals chose to support Ocatvius (who was 18 at the time, but displayed good political insight) which resulted in the subsequent civil wars and the end of the Republic/start of the Principate.
I'm at work, so this is a quick answer and I gloss over some stuff to keep it short. When I'm home I'll edit this and add some interesting reads on the subject.