RAV4 is more than enough for KKH. I have travelled on KKH and Skardu Road a number of times in my Suzuki Alto.
Yes, there are workshops and tyre shops but I have never experienced their services (Thanks to my fit as a fiddle ALTO). Also don't worry about petrol. Just don't forget to fill your vehicle's petrol tank in Besham and then in Chillas.
If you decide to stay in Besham then PTDC motel and Besham Contenantal Hotel are good choices. If you need to stay in Chillas, don't go inside the city. You will find some good hotels along KKH in Chillas. You can choose a hotel depending on your pocket.
For Fairy meadows you have to leave KKH from Raikot bridge (some 2-hour drive from Chillas).
From Raikot bridge to Jaglot, road is excellent. (30-minute drive)
For Shangrila Resorts Skardu, you will leave KKH 5 km after Jaglot town (Fill your vehicle's petrol tank in Jaglot. Shell, Total and Caltex petrol pumps are at the end of the town) and will take Skardu road (five-and-a-half-hour drive). Shangrila resort is some 30 kms before Skardu city. Stay at Shangrila is expensive. If you want to save money just visit the Shangrila and stay in Skardu city. There are some good hotels on the main road.
You should spare at least one week. If you can manage more then it is better. You can visit other places from Skardu (Shigar valley, Khaplu valley, Thalley valley, Satpara lake, Manthoka waterfalls, Deosai etc).