Q:

How does CMR work exactly?

I would like to know the actual facts from the TV-show. 

How come Alec Sadler immediately 'tunes in' to Keira's CMR? 
Was he always listening? If so what wireless medium (in the spectrum) and technology/protocol (was this described in the show)?
Can Keira talk to Alec by thoughts rather than speech? He also seems to be connected on the go, is that his phone or computer?

A:

The reason Alec Sadler was able to "immediately tune into Keira's CMR" was because he was already listening on that frequency. It is explained in "A Stitch In Time" that as the inventor of the technology he was already actively listening and testing communications on the experimental frequency which was later used for CMR communications. While all of the functionality wasn't available at the start of this episode (for example, when Keira uploads her daily activity in the middle of the first episode, it appears as white noise at first on Alec's equipment).
The exact protocol and methods of communication was not described in the show, it's obviously some form of wireless communication but information about protocols and technologies used is not stated. 
At no point during the series to date has Keira been able to communicate with Alec by thoughts, in all instances she has had to speak although communication by thought hasn't ever been ruled out as a possibility. There are a few instances where Keira actually uses a cellular device to call Alec and while these make up many of the instances where Keira contacts Alec while he is on the move, when he is "out" but "stationary" (for example one of the many scenes where he is sat in a coffee shop or similar) his laptop is clearly visible so he likely has a copy of whatever software is used by his technology present on his laptop or a direct link to his home machine.
For more information about the Cellular Memory Review technology you can use the following resources;

Continuum Wikia page
Continuum Omnipedia page

