Sorry I don't know anything about the gender question. They have 2 777's 2 747 400's, 1 BBJ, 1 A319CJ and 1 BAE 146.
I heard similar things in regards to lack of scheduling stability.
a bit off topic with the initial question but If you have been offered a FO position at EY, I assume it would be on the 320 (or at least it should be) but given your Boeing background it might be the 777.
If it is the 320 I suggest you really think about it before you take it. the quality of life on this fleet is non existent with very few amount of days off, successive night flights with very long duty periods and multiple rostering changes. morale is extremely low on this fleet. on the other hand the other part of the company (330/340/777) is quite happy.
between EY and EK (if offered the 320 at EY) I would probably suggest EK. the path to the left seat might be longer at EK (though some would argue with that) but your quality of life will most certainly be better than on the 320 at EY.
Good luck