To answer 1:
Almost all of the fee structure goes to players much higher up the chain than Square. The networks take a chunk, but in fact most of the fee goes to the originating bank (the bank that issued the card). This is a major source of income for most banks these days and can generally be arbitrarily set by them since merchants not only have no other options except cash, but also cannot tell what their interchange fee would be prior to accepting the charge (except with a flat rate system like Square). So, because processors (Square) do not control the rates, there is no way for entrants to create any real competition around them.
Not to mention that 2.75% is actually kind of high as an overall average and that the rumor is that Square actually operates these fees at a loss currently.
Now, as for 2:
As I said above, most of the fees go to the bank that issued the card (1.5-2.0%), another part goes to the network (VISA/MC), and the rest to the processor (Square). This is indeed HUGE money. It is literally hundreds of billions of dollars of revenue and profit controlled by a handful of banks. A high-ranking employee at a major US bank once told me that if you break down their corporate profits by division, interchange fees alone account for a significant portion of the entire bank's profits!
So, suffice it to say, if we (the entrepreneurial world) can figure out how to create an interchange free system, its inventors could possibly be some of the wealthiest people in history. I happen to have a strong business plan along these lines and would love to share/discuss it with anyone interested. Let me know!
edit: typo