Ryan, this kit is designed so the top socket connects to the bottom without having to go through a stud with the Romex cable that connects them together. You can do what you note if you have the ability to go through the stud though. Take a look at the instruction PDF in the listing here on Home Depot. There is also another kit without a bottom socket you connect to old work.
There are two supplied cords with the kit. One is a Romex type cord that attaches the upper and lower part of the relocation kit that installs behind the wall. Then there is the extension type cord that links the lower receptacle to an AC source. Epic does not sell the cables separate however, you can purchase longer Romex and or an extension cord from Home Depot.
Yes. The product has lengthy screws which tighten down to the drywall.
Approximately 4.5 inches
Yes, both the surge module and in wall (Romex) wire are UL Certified