1) You can park your car at Shangrilla Raikot or SHangrilla Chillas. Personally i would prefer shangrilla Chillas though. You will have to travel from chillas to raikot on public or hired transport but thats hardly 1 and half hour journey. After Raikot, there is jeep trek of 1.5 hours and then the 5.5 km of hiking or you can hire a horse/khachar. Although , there wouldnt be anything to do in fairy meadows for 5 days.
2) You can go via NATCO bus as well. It is safe. The buses travel in groups in kohistan area. And its relatively safe. There are loads of police chekpost etc.
3) The route through naran and babusar top is better but i dont think it has opened yet. Other route will be on KKH to chillas.