You are not making any sense at all. People don't usually exchange message with their lover via their work phone, no matter what. And if they do, they would have locked the phone with password/pin.
Thankfully Ares is the ML and not other gods. Unlike other Greek gods, he is a devoted one right, and feminist too (very protective of his Amazonian daughters).
Have you tried reading Chinese webnovel before? You'd be surprised at how many of them are like that. Divine Doctor: Daughter of the First Wife's protagonist Feng Yuheng is a good example of blatantly evil protagonist.
I have no problem if she wanted to send him out in order to "groom" him into becoming a competent and credible general. But not as a unit's general if this is his first time in battle.
...they couldn't choose someone else as the genius?
I know about Zhang Lu because I played ROTK before. We will see for now. I am still not convinced that he is good enough to be considered a genius.