If I couldn’t say Havdalah on Motzei Shabbos (eg in a hospital), when is the latest that I can say it? What if I haven’t said it past that time; can I rely on Atah Chonantanu in Maariv or Baruch Hamavdil?

You can say Havdalah till tuesday. If you have said Ata Chonnantanu or Baruch Hamavdil the only thing you cannot do before Havdalah is eat. If you have not said Havdalah by tuesday you have missed the chance and can eat. Rabbi Binyamin Bamberger