Yes. However, Wi-Fi.org does not release information on who fails their compliance tests.
I like cheap. I guess cheap hardware doesn't have model numbers.
I'll assume you've checked for updated router firmware and Edimax client drivers.
Yep. The problem is that the WEP conversion from ASCII to Hex keys is different between different manufactories. There should be only one way, but since standards are such a great thing, every company wants to invent their own. Setup the unspecified model Actiontec ADSL (wireless?) router for 128bit WEP and use a Hex key, not an ASCII key. That always works. (Yeah, I know it's a big long key, but I can't do anything about that).
WPA should work without the same problem as the ASCII to Hex conversion has been standardized. If your unspecified Edimax card does not work with WPA, then something is wrong with the driver (WPA is usually in the driver, not the hardware). You might want to try an alternative WPA driver before you give up.