1) The point is all your chest thumping about how you'd "refuse the search" and "these searches are violations of peoples' rights" is complete nonsense. It is not a violation of anybody's rights unless we ignore several centuries of case law (making the conduct of the searches Friday a slippery slope with an apparent slope of 0), and for all your noise about refusing the search - you would have had no legal standing to do so. In other words: you are ignorant of how the law functions, and how your rights are applied, as you have quite capably demonstrated.
2) "Hot pursuit" would be a TYPE of exigent circumstance, it need not be present in every case where the officers conduct a search or pursue a suspect. The only requirement for exigent circumstances to exist is "immediate threat" - a clear threat to public safety, the risk of a suspect evading capture, the destruction of evidence.
3) No, you go back and read again. The reason it was disallowed is because the "reasonable suspicion" would not have been enough for the issuance of a warrant, and "exigent circumstances" do not allow you to waive the conditions for a warrant, and search whatever you damn well please. They had probable cause to believe a shooter and a gun would be in the apartment they entered, because the bullet that hit the man in the apartment below *originated there.* They had no probable cause to believe that the stereos were stolen, merely 'reasonable suspicion.' The officer went in, and conducted a search NOT COVERED by the narrow circumstances of the exigent circumstance (the shooting) which allowed him to enter the apartment, and all the evidence gathered was thrown out because he conducted a search NOT related to the reason that allowed him to enter the apartment without a warrant in the first place.
4) An armed & desperate man, who engaged in a series of gun battles with police across Watertown on Thursday evening and Friday morning, who was throwing bombs around in a residential neighborhood - a man wanted in connection with 4 murders, and about 200 counts of assault with a deadly weapon - was at large within the area they were searching in on Friday. This presents a clear threat to public safety, and a clear and immediate risk that not continuing the search would result in him evading capture. Please explain how this does not fall within the definition of exigent circumstances?
You keep making broad assertions about these searches, but you're only making it clear that you have vast misapprehensions about how the law governs warrantless searches, and a vast ignorance of the scenario in Boston that led to them in the first place. It's cool to have opinions, but have you ever considered doing the most basic of research into the facts of the situations you're drawing conclusions about? It'd spare you a lot of this embarrassment, surely.