1. At an individual level, yes, it is easier to enter in Big 4 than MBB. At an aggregate level there was an article about “Deloitte being harder to get into than Harvard”, but I would say that nowadays most job positions are flooded with applications (because, contrary to school ones, they are free) so I don’t believe that statistic is relevant
2. Deloitte is the one with the most developed strategic consulting arm, however EY and others all bought boutique strategic firms in past few years so they are present in the space (Parthenon, Monitor, Booz/Strategy&)
3. Possibile and more and more common. However, interestingly, in my personal experience the transition happens more from the transaction advisory services side or the accounting side of those firms rather than the consulting side.
hope this helps,