Canon 6D Noise

This is a shot from my brand new Canon 6D with 24-105 F/4 L. It was a November afternoon with bright back-lit sunlight and a softbox to the camera right. 1/180, F/6.7, ISO 100. I could not help but notice two issues. Picture was taken in RAW and converted in Canon’s DPP. No adjustments were done to the image, only cropping.

(1) The noise on the collar and other parts of the jacket. It also showed in other pictures taken with the 70-200 F4L IS lens, later in the afternoon under cloudy sky.

(2) The purple color casting on the jacket especially on the right chest side; the color of the jacket is a solid black no matter how you look at it.

What is the possible problem? The lighting or the camera? Appreciate the help!

I am new here and still couldn't figure out how to post. So here it is:

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