I'm 99% sure the games are region-specific, so she wouldn't be able to just take her US games and play them on a system bough in Egypt.
The games are region specific yes.
I'm quite sure you use a NTSC console on a PAL tv. I've heard of a lot of people who have imported their consoles because they usually take ages to be released in EU.
I could play NTSC games on my modded PAL-PS2 with no problems (same with movies).
So PAL tv's can definetly show a NTSC signal, and new tv's (LCD/Plasma) don't use different signals afaik, so I can't see why it should be a problem.