Storyline Course that Branches by Roles

The third bullet is fairly simple. Storyline can send Results slide data to the LMS, though famously it will only send the data from one Results slide per interaction. Fortunately, that's exactly what you're looking for. That can be found in the course's Publish settings:

The second bullet will depend much more on the particular LMS you all are using. In short though, if your LMS can already see the granular per-question Quiz data, then it would be nothing for you to make an extra question that is completed by the course instead of the learner.

Believe it or not, you can make a fill-in-the-blank question, move the input field offscreen so the learner can't access it, and then you can add a text variable to the field as its default value. Each of the branches can update the variable to the role name, and then when that fill-in-the-blank slide is passed through by the learner, its contents will be the variable's updated value. Then when the question is submitted to the LMS along with the rest, the "answer" submitted will be the role that the variable last was.