So, as you might know, my Fubuki recently went from C to EX class (I had been using Howling's leg armor and was losing contantly, I began using Maochao's instead and began winning, but it looks like I was too late.) So, it was reccomended that I reset. So, I heard there was a way to reset a shinki without "killing" it, how do I do this, and where is the option for it once I'm able? I also noticed that the CSCs seem to have levels or something, what do these do?

Only way to reset a shinki without "killing" it is to get it to max level and then do a CSC Restore.

CSCs don't have levels. They can affect your Shinki's level cap though. For example, a Ruby has a chance of increasing your Shinki's max level by 5 or even 10 levels (the standard cap is level 150). The chances of this are rather low. Diamond CSCs have a 100% chance of increasing the cap by 30 levels with a small chance of increasing by 60 levels.