There's not really an age... I start coaching roundoff when they have a good cartwheel and handstand. But I would start by very basic drills, like finishing their roundoff on their belly. For the back handspring, it's the same thing. I start with having them just jump backward on their back, hips toward the ceiling, alone with a rolling mat, finishing on their belly, then with help, finishing on their belly again. I do this in so many different situations: on the trampoline, on a declined mat, from a springboard, in the pit, etc.
For the bent arms, it would be nice to have a video to know why she bents her arms. Is she advancing her knees? Does she throw her head? When she arrives on her hands, are her legs alreardy at vertical? Does she have get good distance and height by herself?