Manga thoughts
With the zanpakutou, knowing the name of your blade is (literally) knowing a part of yourself deeper. Thus, by calling it out, shinigami focus on that part of themselves, resulting in greater power.
As for kido, I think those nonsensical chants are a form of self-hypnosis. The fact that not saying them aloud reduces the kido's effectiveness follows that; if the chant isn't spoken aloud, one of the senses (hearing) isn't involved in the self-hypnosis.
Think of it similarly to a kiai shout in martial arts. They're not necessary, but they do have an effect.
As for Chad's power being "similar to the Arrancar"... I can kind of see why. At the very least, it does share one similarity: Arrancar release their power by way of changing their bodies in some manner, which Chad does. I have to wonder if it goes any further than that.
I like the symbolism of the "Left Arm of the Devil". His main hand is his shield, reflecting his belief that stopping violence is the most important thing. Attacking is a forbidden thing, except when Chad is defending his friends. So, realizing that helping his friends requires him to go on the offensive, he has "made a deal with the Devil", in a sense.
Also, here's an odd note for those who didn't know this: In Latin, the word for "left hand" is "Sinister".