1) Which phone - model and, if possible, model number? There's no Cyanogen for many phones. (The ROM has to be written for that model phone. Flashing a ROM for another phone will brick yours.)
2) Cyanogen is rooted. When you flash a new ROM, the old ROM, including the files installed to root it, disappear (that's all rooting is - installing a few files - you have to be rooted to do it, which is why you need some special way of rooting, you can't just copy files). Rooting then flashing a ROM is a waste of effort. It's like washing your hands just before making mud balls - then washing them again. The first wash was a waste.
3) Unlocking the bootloader depends on the phone. Some can be, some can't be, some don't need anything done to them to flash a ROM.
4) A custom recovery is your choice - you can flash a ROM and stay with the stock recovery (or flash a custom recovery but keep the stock ROM), but you normally want CWM or TWRP because they make it easier to do a lot of things. (Again - you can't install a custom recovery on some phones.)
5) What are you going to get from Cyanogen that you aren't getting from your stock ROM? If it's just the look, you can install the same launcher Cyanogen uses without flashing a ROM (although I prefer Nova Launcher, but which launcher you prefer is a personal matter), unlocking the bootloader, rooting, installing a custom recovery - any of which void the warranty, while a new launcher and new icons and wallpaper don't. If it's some particular feature, same thing - you can probably find an app that will do it. If it's getting rid of bloat, just root (first make sure you have the files and programs you need to reflash the stock ROM [you could remove some "bloat" the phone needs and brick the phone or even brick it by rooting it] and freeze the apps you consider bloat - one at a time. Freeze one, use the phone for a few days and see if there are any problems. If not, uninstall that one and freeze the next one. (You can use Link2SD for both freezing/unfreezing and uninstalling, and it's free.) If there's a problem, unfreeze the app - it's needed for the phone to work. (If you brick the phone - you can't even unfreeze the app without having the app running - you have the tools you need [and, hopefully a link to a thread explaining how to do it] to reflash the stock ROM and not freeze that "bloat" [which you now know isn't] again.)