Hey!
This might differ between firms, so I would always check any instructions that they provide before the VI, but I wouldn't worry about memorising every single figure from the case study. If you are given time to make notes, I think it is absolutely fine to jot down key figures, facts or points that you want to refer back to during the VI.
I would just try to avoid having a full script and reading from it, as that can make your delivery feel less natural. For the figures, I would focus on remembering the key ones that are particularly relevant to your analysis, but there is nothing wrong with briefly looking down at your notes to check a number.
For eye contact, I would aim to look at the camera for the majority of your answer, but I don't think you need to maintain constant eye contact. Briefly looking at your notes to make sure you have a figure right is completely nature. I would prioritise giving a clear and well-structured answer over trying to appear perfectly polished or rehearsed!
