Number 3 is definitely described as "on her stomach". I'd be surprised if anyone has another phrase for this, at least one that they claim is commonly used.
Number 4 we'd say "on her lap". It's a little ambiguous as by "on her lap" we usually mean sitting sideways relative to the person "underneath". But the baby is clearly on her lap.
Number 2 we would say she is "holding the baby" or "the baby is in her arms". I don't think we'd normally say the baby is "on ..." anything here.
Number 1 is probably the trickiest. I think most fluent English speakers would say the baby is "on her shoulder". Yes, that's ambiguous, potentially misleading if taken literally. If the baby was sitting on her shoulder, like with his arms above the top of her head, we'd also say he was "on her shoulder". Though I suppose in the case of your picture we say the baby is "lying on her shoulder" while in the other case I just described we would say he is "sitting on her shoulder". Alternatively, it wouldn't be terribly odd for someone to describe number 1 as "on her stomach".