I believe the 3 month waiting period is to make sure that the woman is not pregnant.
As to the 4 month and 10 day period, I'm not sure.

Also, the Egyptian government just changed the requirements for a U.S. citizen to marry in Egypt through the Ministry of Justice (making it a legal marriage in the U.S.) and it's not currently possible, though the U.S. Embassy website says that the situation is being worked on.
I'm not sure if this applies to citizens from other countries as well or if it's just the U.S.