1. Great question - More important than between companies is between offices (S. Korea is totally different from Indonesia or Singapore for example!). McKinsey and BCG compete on most work. As such, much more determinant of your future is not McKinsey vs BCG, but who you work with and who you associate with in your first few years (i.e. which country/office, which Partners, which vertical). Focus more on this!
Additionally, Bain overall is much more well known for PE/DD work, so keep this in mind.
Finally, this is a fantastic networking question when speaking with each office (i.e. what industries/functions do you see the most of)
2. I think McKinsey is the toughest. They are the "scariest", more math heavy, and less supportive/expressive in their interview style.
3. Network across all 3 - no only will you start to learn these answers yourself but you'll have better chances during your recruiting :)