My corrections and changes are shown below:
Everything, allegedly, started with road rage and ended up as a murder case. The suspect followed the victim to her house where a shooting occurred. According to some witnesess the suspect already knew the victim. Police investigating the case are trying to establish if the crime was directly caused by the road rage or if there was some unknown dispute between them that may caused the crime. Neighbours are outraged because the crime happened in their good and calm community.