Can each person be responsible for paying for their own purchases in Family Sharing?

The payment method for Family Sharing is automatic:

1. If anybody in the family buys or subscribes to something, Apple first attempts to charge the item to that individual's Apple ID balance, if any.

2. If a family member does not have enough personal balance, any excess will be charged to the Family Organizer's primary payment method (usually a card of some kind). The Organizer's personal balance will not be used for purchases made by other family members. If it cannot bill the primary payment method then it will just work its way down the Organizer's list of payment methods until it finds one it can.

- "Some purchases, including gifts, can't be billed to Apple ID balance and will be charged to the family organizer's payment method." "Some subscriptions might not be charged to Apple ID balance."

Ref:

- Family purchases and payments - https://support.apple.com/HT201079

- How App Store and iTunes Store purchases are billed - https://support.apple.com/HT201359

- Check your Apple ID balance - https://support.apple.com/HT202359

What you want is possible but only if people maintain sufficient Apple Account (Apple ID) balance to completely cover the value of their purchases.

Read the links below about various ways to pay for items in the iTunes and App Stores.

- Add funds to your Apple ID balance - "Use a payment method, such as a credit or debit card, to add funds to your Apple ID balance."

Click here --> https://support.apple.com/HT208687

- Create and add money to an iTunes Pass - "At Apple Stores and select retailers, you can add store credit directly to the Apple ID that you use for App Store, iTunes Store, and iBooks Store purchases." - https://support.apple.com/HT203021

- Redeem App Store & iTunes Gift Cards, Apple Music Gift Cards, and content codes - https://support.apple.com/HT201209