What is a hymenal ring and how/when does it break? is it possible for the ring to still be intact even if the hymen has already been broken?

Yes and no.: It is avestigeal membrane at the intritus. Can be perforated ( common), imperforated ( uncommon), elastic ( to accomodate penetration ), rigid ( obstructing penetration ). Usually ruptures with first penetration ( intercourse ), can cause bleeding ( so called proof of virginity ).

Hymen = hymenal ring: The hymen and hymenal ring are synonymous so it isn't possible to have one be broken and the other intact.