OK here's the wording from my OPLIMs I received back in Apr 2015 which is verbatim out of 8130.2G (yes I know there's a 2H, but the Washington FSDO is still referencing the 2G verbiage):
(6) This aircraft is prohibited from operating in congested airways or over densely populated areas unless directed by air traffic control, or unless sufficient altitude is maintained to effect a safe emergency landing in the event of a power unit failure, without hazard to persons or property on the ground.
Note: This limitation is applicable to the aircraft after it has satisfactorily completed all requirements for phase I flight testing, has the appropriate endorsement in the aircraft logbook and maintenance records, and is operating in phase II.
(7) This aircraft is to be operated under VFR, day only.
(8) After completion of phase I flight testing, unless appropriately equipped for night and/or instrument flight in accordance with 14 CFR § 91.205, this aircraft is to be operated under VFR, day only.
(9) Aircraft instruments and equipment installed and used under 14 CFR § 91.205 must be inspected and maintained in accordance with the requirements of 14 CFR part 91. Any maintenance or inspection of this equipment must be recorded in the aircraft logbook and maintenance records
Basically what this says is if properly equipped and maintained you can operate an E-AB pretty much like you would any aircraft once you are in Phase II. Case in point, I just completed a 790nm IFR trip from Florida to Virginia this afternoon in my RV-10.
As far as training is concerned, if you own it you can train in it to include an initial rating (ie Private or Sport Pilot). With a LODA, a CFI can conduct training in their E-AB aircraft and charge for it.