Private Car should be preferred if you have budget. No enjoyment on public transport. Driving your own car is also very thrilling on those hilly roads and you can stay and enjoy wherever you want to. Corolla is best. If you want to rent a car on self then it would be your personal resources and if with driver than go to Car stand in your city and every one will be happy to go with you.
Rent info:
On Self - 3500/day Corolla
With Driver - 6K for first day and then 3K/Day.
From Day 1 to Day 7, approximately fuel of 10K price would be consumed. Don't know about that, whenever i visited naran , styaed in different hotels and on searching less stars hotel and negotiating prices , I always get a room for 3K/Day.
As far your Plan, it's good except Day 5- Day 6, it is accessible but the advice is to give it a more day to enjoy the scenery. If you want only an overnight camping and nothing else, than go for it.
