Electrical Panels – Where Arc Fault Breakers Should Not Be Used

First off. The only way to provide proper "grounding", is to install a grounding conductor from the panel to each outlet. Providing AFCI and GFCI protection to the circuits is helpful, but these devices will not provide "grounding".

If you switch from 2-prong receptacles to 3-prong on these circuits, you should not connect anything to the grounding screw of the receptacles. You should also (technically) install labels at each outlet that read "GFCI protection" and "No Equipment Ground". Though, these labels aren't common in residential situations.

1. Replace GFCI breakers with CAFCI breakers and add GFCI receptacles to the first-outlet on each circuit.

This is probably going to be your best bet. In this scenario, the CAFCI breaker provides protection to the entire circuit. The GFCI protection being at the first outlet, means that while the wiring from the panel to this location is not protected, the rest of the circuit is protected.

2. Keep GFCI breakers and add AFCI receptacles to the first-outlet on each circuit.

This isn't a terrible option, although the AFCI device will not be protecting the wiring between the panel and the device. Also note that an AFCI device only detects line to ground arcs (parallel arcs), while a CAFCI device detects both line to ground and line to line arcs (parallel and series arcs).

3. Replace GFCI breakers with Dual Function AFCI/GFCI breakers.

If you could actually find these (and could afford them), this would probably be your best course of action. Unfortunately, these devices probably don't exists (yet) from most manufacturers.

This behavior is because arc-fault breakers have an interesting quirk: they also provide a small degree of ground fault protection as well! (They are not GFCI's because their ground-fault trip threshold is set to the 30mA used for equipment protection (GFPE) devices as opposed to the 5mA ground-fault (differential) trip of a Class A personnel protection GFCI.)

You will need to contact your electrician and tell them to get their neutrals straight. Tell him he violated NEC sections 200.4:

Multiple Circuits. Where more than one neutral conductor associated with different circuits is in an enclosure, grounded circuit conductors of each circuit shall be identified or grouped to correspond with the ungrounded circuit conductor(s) by wire markers, cable ties, or similar means in at least one location within the enclosure.

300.3(B):

Conductors of the Same Circuit. All conductors of the same circuit and, where used, the grounded conductor and all equipment grounding conductors and bonding conductors shall be contained within the same raceway, auxiliary gutter, cable tray, cablebus assembly, trench, cable, or cord, unless otherwise permitted in accordance with 300.3(B)(1) through (B)(4).

and 310.10(H)(1):

General. Aluminum, copper-clad aluminum, or copper conductors, for each phase, polarity, neutral, or grounded circuit shall be permitted to be connected in parallel (electrically joined at both ends) only in sizes 1/0 AWG and larger where installed in accordance with 310.10(H)(2) through (H)(6).