18 How did the Roman Republic turn into a dictatorship?

It was an extended process. In the first instance the Roman Republic had a specific legal role for a 'dictator', typically one elected for a six month period and was periodically installed in times of military emergency or domestic upheaval.

The process of 'subversion' of the Republic finally resulted in an Imperial regime beginning with Octavian (Augustus) 30's BC to 14 AD - though for centuries some nominal form of a 'republic' was maintained. For many years previously populist and generals would instigate forceful regime changes which with each incident tended to undermine the stability of the Republic.