I'm biased.
1. It's better to graduate from a service academy, but that doesn't mean it isn't good to graduate from a semior military college. Service academies are focused, more, on a specific branch of the service, obviously, so it's more concentrated. I think they're also better known. Again, remember, I'm biased.
Yes, there's some "baggage" that comes with being a "Ring Knocker," but that fades.
2. Yes. Same country, but you'd be smart to pick up some popcorn and watch 'em duke it out during budget season.
3. Yes, it does matter where you graduate from, but that's true of any school. Better schools have a tendency to, if not open doors, get second looks from employers. What you'll find at service academy and senior military colleges is a great network out "in the real world". I assumed that was hype. While I was in the Coast Guard, 45% of our officers went to the Coast Guard Academy, so it wasn't that big of a deal.... but when I got out, I got to experience that network firsthand, and it made me pretty proud.
As Jcleppe said, once you pin on those butter bars, it's on you. True you may have some classmates here and there, but your diploma won't buy you good reviews and promotions... you have to work for that... whether you went to an academy, a senior military college, through an ROTC program, through OCS or a direct commission program.... it's on you, sink or swim.