Well, I am pretty sure that the turbo will work on a 2014 Corolla with the 6 speed manual. As for the CVT band, email Toyota since they should know whats in this transmission.
Well, if you want to see how much power from the turbo the CVT can handle, why not start at a low boost pressure and work your way up until you feel like it is producing a good amount of power and is still safe for the CVT.
I don't think those will fit the 2014 Corolla. Those look a lot more like the ones on this 2011-2013 Corolla S than the one the 2014 Corolla:
Although I could be wrong...:unsure:
Hey guys! I just wanted to introduce myself into this forum.:D You may know me from ToyotaNation as SupremeCorolla451. I have a love for Corolla's and I own a 2007 Corolla CE!:thumbsup: It's great to be here!:clap: