Can females drink alcohol and smoke cigarettes freely in public in Egypt?

Deapends how your define "public" and where you're going. Cairo, Luxor, Nile cruises and the Red Sea resorts, no problem - except that, as a Muslim country, Egypt is technically dry, so you won't be able to buy beer in a supermarket, for example. However, the majority of hotels have a bar (or bars) and serve alcohol without any problems - they also do some wonderful non-alcoholic cocktails, too. They're worth trying just for the taste!

Cigarettes I'm not so sure about as I don't smoke, but I had a freind who did - and she smoked quite happily all through a Nile cruise.