I don't have an AV Famicom, but I do have the original model and it's power adapter works fine here in the US.
DO NOT UNDER ANY CIRCUMSTANCES USE AN NES POWER ADAPTER!!!
Famicom power adapters convert the wall's AC to DC before it enters the system.
NES power adapters do no such thing, as it is handled inside the system itself.
Basically, you'll fry the thing.
The AV Famicom will be 100% compatible with all US games (if you use a pin adapter) except for games that use nonstandard controllers. Although it uses the same controller ports as an NES, some pins (used by the lightgun for sure, but probably other accessories as well, possibly including the fourscore) were left unconnected to the system board since such accessories in Japan use a very different port (found on the front of the original Famicom and the right side of the AV Famicom). This is very easily mended with a little bit of soldering.
The AV Famicom will also be 100% compatible with all Japanese games, including Disk System games (provided you buy a Disk System to play them on).... except for those very few games that use the microphone on the original Famicom's second controller.... Which is mostly not required to complete the games. (The FDS version of Zelda 1 and Takeshi's Challenge are the only ones I'm aware of that'll really cause trouble)