Is CyanogenMod rooting the phone? If I install CyanogenMod, will I have 'rooted' my phone? Is CyanogenMod a rooting program, or is the procedure of installing CyanogenMod rooting, and CyanogenMod is something needing root?

Is CyanogenMod a type of android release? Considering to install it is similar to a new android update?
for 99% of devices, you have to have a custom recovery image installed on the device in order to install CyanogenMod. And usually, to do that you have to have the device rooted. So you have to have a rooted device before you can install cyanogenmod. 

CyanogenMod comes rooted and yes, it is an android release. Rooting a device, while it will void your warranty, is not really that "bad". Think of it like having access to the administrator account on your PC as opposed to a "limited user" account. 

You also have to keep in mind that CyanogenMod does not work on all android devices. You can only install it on devices that are supported.