I echo all the comments about the dress code here. Of the approximately 40 Egyptian women working in our office, only two wear a scarf. Most are in trousers and tops that would fit in anywhere. Trousers and a long sleeve shirt should be sufficient for all places except mosques, where you should have a scarf. (Though I have been in to many mosques with western friends who have not worn scarves and there has been no issue).

Regarding the airport, I would advice the "meet & greet" from whichever hotel you are staying at. It helps getting through the chaotic immigration area, and particularly for ground transportation- the regular taxis have been moved away from the terminal due to construction of the new terminal, and you would have to take a bus to get to them. If you opt for taking a cab, you are better off with the private cab companies just to the right of the Customs exit. You will have to negotiate slightly with them, but 50-65LE is the rate for the downtown hotels.