Yes, I will. How much they receive will depend on what their chore is. If their chores contributes to the family (such as aiding in cooking), they will receive more finances. If they are just sweeping the floor, which could take 5 minutes since there is no carpets, and there is a cent-vac system, then their chore is not as intense, and they will receive less. I will also reward good behavior, but will be sure to remind them that society does not reward good behavior.
Also, if the child was to receive a contribution of finances from family, or loved ones, then they will receive that. I will doubt any inheritance or gift will be enough to cover for their expenses, so they will likely need to do their chores, and be on good behavior to receive the money they will need to get the things they want or need.
Money received from CYS (Children & Youth Services) will contribute to their food bill. With that said, I would not add the additional costs to my food bill in my budget of the various sites regarding my windfalls. As for health insurance, I will assume as a ward of the state, they will receive Medicaid which I will choose the UPMC supplemental plan.