Regarding the sa'angreal issue, Egwene al'Vere does not share power. She is kind of ego-centric, so letting someone else have the rod to increase the power of the circle is probably not as important to her as having the rush herself.

Another radical unsustantiated claim... which is also why she gave the angreal in the storerooms to the other Aes Sedai. According to you she should have just piled them on to herself.