If I log into my childs icloud on my iPhone would I also receive her messages?

Also would she be aware of this If I did? I'm just monitoring her to make sure she is safe.

You can also turn on restrictions, use a password that can't be guessed so have letters and numbers both in it.

Get some smart parental control apps for cell like spyphone:

it helps track kids' messages without user noitce.

Yes, and possibly. Sure you are.