Vavso,
Flight Standards District Offices do not set, make, or interpret regulation. FSDO's administer the various programs of the FAA, and initiate enforcement actions. A FSDO, or an inspector at the FSDO level, cannot interpret a regulation with authority, nor can an inspector enforce a regulation which does not exist, or has been altered. The FAA is bound by the FAR every bit as much as certificate holders are.
Practice approaches are legal to conduct without any authorization outside Class B, C, and D airspace. In areas where ATC authorization is required, practice approaches must receive a clearance, and when conducted under VFR, are subject to the same limitations as any other VFR flight.
Practice approaches when conducted under IFR are subject to the same limitations as any IFR clearance, and any other IFR flight.
Practice approaches are instrument approaches, and may be approved by ATC subject to traffic and workload conditions. Pilots performing practice approaches under VFR will be instructed to remain VFR. Pilots desiring practice approaches under IFR must specifically request a practice approach, and must receive an IFR clearance. ATC is not obligated to grant this request.
At airports without a tower, pilots who wish to make practice instrument approaches should notify the facility having control of the desired approach, as indicated on the approach chart.
VFR aircraft executing practice instrument approaches are not automatically authorized to conduct the missed approach proceedure. This authorization must be specifically requested from the controller. Separation will not be provided unless the missed approach has been approved by ATC.
Aircraft cleared for practice approaches must not deviate from the clearance, except in an emergency, or unless the clearance is ammended or the deviation approved by ATC.
See AIM 4-3-22 for details on practice approaches.
You asked about requesting a practice approach, and what facility to use. If you are airborne and talking to approach, make your request with approach. If you are on the ground, make your request with clearance delivery, ground, or the tower, as appropriate. If you intend to execute the practice approaches under IFR, you must obtain an IFR clearance to do so. (Remembering that IFR means instrument rules, not conditions).
Center or approach can deny a request for IFR during a pop-up clearance, workload permitting. You may be instructed to remain VFR. Again, there is a difference between flying IFR approaches, and instrument approaches. Instrument approaches may be conducted in instrument or visual conditions, under IFR, or VFR. However, flight under Instrument Flight Rules (IFR) requires an IFR clearance, an aircraft approved for IFR, and a pilot in command who is rated and legal to fly under IFR, and current under IFR to act as PIC.
Can approach deny your request for practice approaches? Yes.
