Welcome to PW
1-best route
Lahore - M2 - Burhan Interchange for Hasan Abdal then use Abbottabad road. Use right side Mansehra bypass and continue to Balakot and then onwards to Naran.
2-i have Liana, views abt liana to visit northeren areas as i am little hesitaant after listening from some friends who recomend not to go on liana
All sorts of cars can go till Naran. Road is perfect till Balakot and good till Mahandri. Some bad patches are there between Kaghan and Naran.
3-Naran Hotel Stay and its rates
May end would be pre-season so you should get a good hotel for 1200-1500.
4-Weather of Naran
Chilly and nights would be real cold so keep enough warm clothing for kids.
5-Road Conditions from Lahore to Naran, my liana has 14 inches rims, so wheter its feasible going on it.
Car specific stuff can be answered by some car experts
6-Self cooking is preffered or not ?
People do that to enjoy family outings. Its up to you. Food will be easily available in Naran.