7-8 dayz r more than enuf for neelum valley and noori top but if u wana trek than u need more time as ratti gali and saral lakes are two dayz treks each........
regarding kashmir u can reach kel and shaunter on ur prado. time from muzaffarabad is such u can reach kel in one day from muzzafarabad. no need to camp in between except u can stay and look around in sharda 1 day if u want........
then shaunter and taobat are 1 day trips from kel each......
Ratti Gali lake will be fiull of snow in early july but reachabvle.
saral will be open fully......
u can easily cover all these areas excpet treks in this time. if u wana trek u shud stop at dowarian and trek to Ratti gali lake. return next day and move forward in jeep to sharda kel. on return from taobat and shaunter u can take noori nar pass which i think shud be open in early july. from nboori top u can trek to saral lake