It is impossible to distinguish between "Это возможность" and "эта возможность" when you hear this. It is not a bug. "о" and "а" pronounced identical when unstressed but when you don't have context, you have low chance to guess right.
This. Either this one maybe shouldn't be an audio-only exercise, or it should accept both.
Is it really that wrong to answer "it is a possibility" instead of 'opportunity'?
Yes, would be interesting to have a commeng form a native speaket because it is really the way it is translated in French : "possibility", that can be either considered as positive (then synonymous to "opportunity") or not, with a neutral meaning ...
I'd say it's closer to possibility than opportunity. Opportunity is more like "шанс".
They are pretty different words since opportunity carries a positive context while possibility is neutral.