1) But most supermarkets do this in similar ways. Not quite the same as a single entity, but close enough (more like a cartel?) that I'm not sure I see much of a difference.
2) This is the major difference in my mind, but other vendors can still sell for less, so I'm not sure how much competition is stiffled.
3) Well, they actually are. It's called slotting fees. They can simply be for warehouse storage and a place in the store, or at higher levels can be paid to have products placed in specific locations, e.g., eye-level on shelves. This seems similar to signing up for the program in the OP to have your product highlighted as an Amazon-sponsored product.
I don't like many of Amazon's practices, but I'm not convinced this particular one rises to anti-trust.