Is my Dependent Care FSA Administrator allowed to deny my claims because the date of service (in the 2019 taxable year) is before the date the FSA was opened?

This is not really a tax question as much as it is an employment law question.  Please contact your HR department or your state insurance department. 

Can I use my FSA to reimburse outstanding medical expenses from the prior year?

No, expenses must be incurred during the current plan year.