If a permanent taps for CC do you get CCC? I am going to assume yes but the wording makes me wonder.
That is correct, this will only add an additional C but that can go quite a long ways. This is effectively a Colorless Caged Sun for one less mana, an addition +1/+1, bonus mana on all permanents not just lands and some tacked on lifegain. That's pretty damn good if you ask me (was going to compare it to gauntlet of power but that hits everyone not just you.)
In what universe? If you build a deck like that, and ever draw that hand, I will personally come to wherever you live, perform complicated acts of awestruck ********, then disembowel myself to escape the world that allowed something like this to occur and validate you.