FAA doesn't do NDBs anymore
The FAA can test you on whatever equipment you have in the aircraft, so if you have an ADF its up to the examiner if you shoot an NDB approach. If you have an autopilot coupled to an IFR approved GPS he is within his rights to ask you to conduct an autopilot coupled GPS approach (best to stick INOP on both of those before the check ride
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Swings and roundabouts really. Some things are harder under JAA and other things are harder under the FAA. For the CPL ME check ride the FAA examiner get you to plan and start flying a VFR flight somewhere (had Vegas for mine), then divert you at some point, VFR. All the time he'll randomly pull the mixture on one or the other engines, and expect the engine failure drill. This can be in the circuit, on the runway or in cruise flight. He'll also expect an engine shut down, whether he asks you 'shut down an engine' or just pull the fuel selector is up to him. For me he just turned off the fuel to one of the engines without me seeing, and as I wen't the engine failure drill I continued to full feather. If he doesn't want it he'll stop you before you you fully feather. They also expect a Vmc demo, and the usual stuff, stalls, steep turns, emergency decent plus a load of pattern work (short field, normal, asymetric etc). If you haven't already got a private ME with instrument privileges, then to add instrument privileges to the ME CPL you need to shoot two approaches, one asymetric....assuming you are already IR'd of course.
If you have the ME CPL, to add the SE privileges you have to do the usual stalls (power on, power off, turning) / steep turns, steep spirals, Eights on Pylons, Lazy 8's, Chandelles, pattern work (normal, short field, soft field, flapless all to within 100' of intended landing point).
If you are taking the initial in a SE, this must be complex, and is basically the SE add on above with the above VFR nav portion as well.
Cheers
EA