I think the reason why Cersei didn't comparatively grieve over Tommen is because of the prophecy. That old witch told her all three of her children will die. After Joffrey and Myrcella died, it is possible she turned rather fatalistic towards Tommen, believing that he would die regardless of what she did.

I'm not saying Cersei wanted Tommen to die, just that she didn't consider at all what her actions would do to Tommen's mental state. All she had to do was console Tommen, talk him down and explain (somehow) that she did what she had to do. Even if Tommen killed himself regardless, she didn't even make the attempt. The Mountain doesn't seem to me to be a good therapist.

Ultimately, her lack of understanding for Tommen is what killed him, perhaps coupled with underlying fatalism regarding his chances of survival in the first place. It fits her character though, as she was always more fixated on Joffrey than the other two.

As for who will kill her? I imagine a long queue forming. I wouldn't be surprised if she killed herself at the last in order to spite whoever wanted to deal the killing blow. If not a Cersei suicide, then probably Jaime. It fits the whole 'tragic romance' theme surrounding them.