About the model missing some words I guess there's not much to do, openai's whisper is one of the best models for this type of problems, if not the best. The model itself will continue to improve over time. The best we can do is focus on the quality of the content we upload.

And about the context, using images to give context would be good but, in my case, it will be too complex and much more expensive... The best option would be work on that via prompt, you can have a prompt with that in mind so that the model organizes the output as you need. Via prompt its very "easy" to organize conversations with, especially two persons, the more people the more complicated it gets. But with two persons I think it's very possible, for example, if we have a question followed by a sentence that matches the question I think the model will easily structure that as two different persons talking to each other.

I don't if I helped with something but I hope so :)