It depends. In most cases they cannot, but there are situations where they can (such as "hot pursuit" or other "exigent circumstances").
The other important question is what can you do about it if they do. The answer is usually not much. It will not be a defense to the underlying criminal case. It may make for a successful motion to suppress if evidence of a new crime is found after the illegal entry or there are damages.
Yes. It's written right into the law.
RCW 10.31.040: To make an arrest in criminal actions, the officer may break open any outer or inner door, or windows of a dwelling house or other building, or any other inclosure, if, after notice of his or her office and purpose, he or she be refused admittance.
Please don't consider this free information to be legal advice. If you want legal advice, you should retain an attorney.
With legal analysis the devil is in the details. This is why you should always consult with a lawyer for any specific legal situation. You have two previous answers that seem to contradict each other. One tells you that probably the Officers cannot break down the door and the other gives you the specific statute that allows them to do so. What's missing? The key to this analysis is: What information do the Officers have that you are in the location? A random deranged person can't say some person with an arrest warrant is in a building resulting in the police lawfully breaking the door down. Of course, you may not know what information the police have. Needless to say, if it's your residence and you answer or they see you in the window the odds greatly increase that they'll break the door down.
At your service,