Well if you are wanting to kill a lady bug, I don't think it is going to matter if it is non-toxic or not. You can smush them with your foot. You might try one of those sticky things that hang down that you can use to catch flies with.
Yes. They compete with each other for prey such as aphids, mealy bugs, mites, scales, and whiteflies. If they've no other food source, then they turn on each other. This is particularly a problem...
"Non-toxic" generally means non-toxic to animals and specifically to humans.
It's possible for something to be more or less innocuous to animals but highly toxic to plant life. Copper, for example.