If we share the family plan can everyone still have their own Apple ID on their phones?

Yes, that is the idea behind Family Sharing. Everyone has their own Apple ID but can still share selected things. More information in:

What is Family Sharing? - Apple Support

and

Set up Family Sharing - Apple Support

and

What types of content can I share with my family using purchase sharing? - Apple Support

Yes, that is one of the primary benefits of Family Sharing.

"Family Sharing makes it easy for up to six family members to share App Store, music, movie, TV, and book purchases, subscriptions to Apple services like Apple Music, Apple TV+, Apple News+, and Apple Arcade, and an iCloud storage plan — all without sharing each other's Apple accounts."