Can they even feed themselves, as a country? I thought that was one of their big problems.
Correct. Among other things, Egypt is the world’s largest importer of wheat.
If you do a web search for “Egypt food imports” you can find all sorts of info., all of it depressing. The basic problem of too many people for not enough arable (or developed to be arable) land is compounded by internal strife and heavy government intervention in the economy.