I wrote "Ráno kávu neměli" - this is a mistake! The correct option is 'neměly'. 'The following sentence from lesson "Ne, včera už příliš nepili". In both cases we are talking about some sort of "they". I've ceased to understand anything....
"Ráno kávu neměli" - the"i" shows that we speak about a mixed group or a group of men.
"Ráno kávu neměly" - the"y" shows that we speak about a group of women.
So without a context the both options are correct.
Is "neměli" in Czech used in the same way as in English, i.e. "they did not have" meaning "they did not drink (or take) coffee" instead of "they did not have (= possess; have at their disposal)"?
It can be used in both examples you have mentioned. Depends on context.
"Ráno jsme kávu neměly" is closest to the sentence in this exercise. The difference is the addition of the auxiliary form, because your example is in the first person. See the Tips & Notes for Past 1: https://www.duolingo.com/skill/cs/Past-1/tips-and-notes