Hi,
I have the same Motor & ESC in my E6, on the battery input into the ESC i am using the EC5 connectors and on the ESC connection with the motor i am using 5.5mm Castle Bullet Connectors.
To secure the ESC to the carbon plate i use sticky velcro so that it secures the ESC but also allows it some movement and it can be removed easily if needed. I also use a small velcro strap around the ESC and carbon plate to secure.
Cheers
Ross