I work in Milan in MBB and I can tell you that there no much difference from one another in terms of work/life balance. A good life-style project is one that starts at 9am and ends at 9pm. But it is a very good lifestyle, you can also have projects that starts at 9am and end at 3am every day. It can happen and it is very difficult to "avoid" them. You can try, knowing people, being proactive, but there is no guarantee that you'll not be staffed in terrible projects. Thus, if you don't think you can accept this risk and this kind of lifestyle, look elsewhere for your career. The job is demanding also in terms of your life outside work, that's one the reasons why consultants are so well paid :) MBB are great career accelerator, but you have to take into account that a few years of your life are going to be tough.
- Both BCG and McKinsey has a dedicated digital practice, thus I would say both of them. Honestly, don't know about Bain
- I think BCG is bigger than McK, but McK is the most prestigious one. That's why salaries are a bit lower than BCG: the brand is part of the benefit, it's going to open more doors that other's when you want to leave
- The internship is usually 3 months. You are working exactly as a BA, but with a lower salary. Since the process to hire is the same from internship and full-time position, it is highly probable that you'll get an offer for full-time position after the internship.
If you want to know more about life in MBB in Milan send me a message and I'll answer all your questions!