1). Yes they are civilians. Yes they have rights, but fewer than most other citizens (although not as bad as the miltary).
-Police officers do not have 1st Amendment rights. Except in the case of political speech related to a labor organization, a department can curtail your speech.
-Officers do not have 2nd Amendment rights. The agency can and does regulate what you can carry and use, even off duty or in your own home, even if the officer obtains a normal concealed weapons license in their state.
-Officers do not have 4th Amendment rights, either. Internal Affairs can make a warrantless search of your person, vehicle or house, without probable cause.
-Officers do not have 5th Amendment rights; they can be forced to talk to investigators, they can be forced make incriminating statements about themselves and can be forced to take polygraph exams. They have no right to counsel during these interrogations.
Who will fight for my rights?
2). Yes we should be held accountable. We even have special laws. Most states have offenses (wiretapping, civil rights, official misconduct) that can only be comitted by an officer, but do not apply to non-LE citizens. When officers are not prosecuted for other criminal acts, this is wrong. This does happen, but I think you will find that law enforcment officers disagree with it; when a law enforcement officer commits a crime, it makes all of us look bad, and we want to see them punished even more than everyone else. A lot of non-prosecutions probably result from political collusion between DAs and agencies; agencies don't want prosecutions because of civil liability-DAs go along because an elected DA is a political animal. This isn't right, its politics.
Yes they are treated differently. They have policies and procdures which they are held accountable for.
3).This may be splitting hairs, but officers do not have weapons that the public does not, but law enforcement agencies do, and the agency can authorize the use or issue those weapons. For that matter, it is all stuff that is available to the public, as well, in most states. Law enforcement just pays the actual price, while civilians, unfortunately, pay the inflated post MG-ban price. I wish it were not that way, because it also puts personally owned MGs out of the price range of most LEOs, and we are mostly shooters and like such things.