The device is maintaining a short (<1 sec) buffer at all times. The device is Echo; Alexa is the cloud-side service, which is definitely not getting the audio until the wake-word is spotted and then streaming begins (backing up to the beginning of the buffer).
Incorrect. Police asked Amazon for a murder suspect's Alexa history, and Amazon initially refused until the suspect/customer gave permission. It is yet to be proven if anything was recorded without the wakeword.
All we know is that the recordings were requested by the prosecution; we have no idea what, if anything, is included in them. In particular, we do NOT know if anything other than the wake word, followed by a few seconds of query, is included. Everything else we've learned, including Amazon's own statements on what is recorded and transmitted, suggests that nothing else is included.