As to the info you're seeking: Google is your friend. (or try 'Bing'.)
the hospital would of course treat a botched abortion that came to the emergency room. If she needed admission, one of the staff admissions would admit her.
This means that if the kid was born alive, he would be saved.
And if the mom was a victim of gross malpractice, the admitting physician could report it to the state medical board as malpractice...whereas if the abortionist admistted her, he could leave the kid in the corner to die and fudge the documents to prove nothing was done wrong.