It definitely is possible to use N-Gage in the US as there are American bloggers who regularly comment on N-Gage games (Ricky Cadden on the Symbian Guru site for example).
In theory the US versions of the N95 and N95 8GB don't support N-Gage yet. However, there are other N-Gage-compatible models such as the N82 and N81 which are available in the US and are officially supported by N-Gage.
More models will be added over time (the N78 and N96 will probably support N-Gage in the future) but at the moment these are the only compatible models.
You asked about which phones would work in the US, well pretty much all of the N-Gage-compatible models will work there as they have triband or quadband GSM (2G) so they work worldwide.
It's the 3G frequencies, which offer broadband mobile internet speeds, that are often US-specific, because the US uses a slightly different set of 3G frequencies to most of the world. That's why Nokia often makes US versions of certain models so that they work with US frequencies.
If you get an N82 or N81 you should be able to install the N-Gage application yourself, see this tutorial for info on how to do it:
Once you've got N-Gage installed on a compatible phone, you can buy the games by credit card, or if your network operator supports it you can buy the games through your phone bill.
The games themselves can be downloaded directly onto your phone through its wi-fi or phone network connection, or you can download them onto your PC from the n-gage.com website and then transfer them onto your phone with a USB cable or Bluetooth connection.
If you're going to use the N-Gage online features such as multiplayer gaming, you can do that through wi-fi at home for free, but if you do it through the phone network you may want to check with your network operator what their internet charges are first. Some of them will offer special deals where you pay a flat monthly fee and they let you use the internet without any limits, it's worth asking if they offer something like that.