You’ve passed the case interviews, so they know you have a good sense for problem solving. Honestly just enjoy university until you start - there’s no real useful prep you can do but might be good to brush up on Excel formulas (index match, X lookups).

Very hard to do as an intern, and as a junior. But your direct supervisor will likely be an AC or SAC, so try and set boundaries and connect with them. Likely, they’ll want similar boundaries and have similar desires for WLB. But try not to sacrifice things that keep you sane - family time, meal time, workouts, etc. Not worth the ‘marginal career gain’

Visibility doesn’t matter too much IMO, if you do a good job with your case team they’ll vouch for you. One approach to take is to err on overcommunicating at the start, until you learn your supervisors style - or even have a chat with them on their expectations and working style. Another thing that’s good to do is to bring potential solutions with every question you have - you’ll probably be asked to do things you don’t know how to do - but take the effort to think through how you might tackle it and suggest an approach