While - as said above - you can only "share" leve quests (both / all of you need indeed to pick them up from leve quest NPCs using your allowances) and once one of the party members will activate the leve you'll have it shared (it will even notify you on the screen). However even just playing together in the party with only one of the members receiving the rewards for completion of the actual quests is beneficial as (apart of helping each other obviously) you're all getting XPs for any party kills or hunt log kills, most likely much more chain bonuses plus - biggest reward - you're playing with the friends.