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.