There are essentially four “Concierge” models:

Fees for care. In this model the fees charged are directly related to medical care, as described by the IRS, and would generally be considered as eligible medical expenses under the HSA guidelines.
Annual Physical. Here a fee is charged for an annual physical, usually comprehensive in scope, that includes no [...]

 
Yes. IRS Notice  2008-59, Q&A 33 addresses the question of a dependent being claimed by a former spouse.   
Q-33. Do qualified medical expenses for HSA purposes include the § 213(d) medical expenses incurred by an account beneficiary’s child who is claimed as a dependent by the account beneficiary’s former spouse?
 A-33. Yes.

Yes – the majority of HSA restrictions center around contributions to the HSA with fewer  restrictions on the withdrawals. In answer to the  question above, money in an HSA can ALWAYS be withdrawn tax-free for the medical expenses of the account holder (also known as the account beneficiary in the IRS regs), the account holder’s [...]

No; An account beneficiary may defer to later taxable years distributions from HSAs to pay or reimburse qualified medical expenses incurred in the current year as long as the expenses were incurred after the HSA was established. Similarly, a distribution from an HSA in the current year can be used to pay or reimburse expenses [...]

Partial List of Qualifying Health Care Expenses
The following list, while not intended to be all inclusive, illustrates medical or medical-related expenses which may be reimbursed tax-exempt under a Health Savings Account.  IRS publications 502 and 969 provide similar information. Section 213(d) of the Tax Code contains the full provisions of the applicable tax deductions.
 
Abortion if [...]