Sounds like a fun project. Here is my advice, for whatever it is worth.
In any case, I would add a 2x4 or some sort of backing to the drywall and run the shanks through them. Use polyurethane adhesive to keep the 2x4 in place, pre-drill/pre-fit it all, before drilling the drywall. Otherwise, just through use and opening closing taps with any sort of force, your drunk friend hitting them, etc, I can see the drywall crumbling around the shanks. Without any support for them, the drywall will ultimately give way.
Use 5/8 inch moisture resistant drywall, or wet rated backer board if you are going to prime/paint.
I would use an insulated box to enclose the entire run. You did not mention how long your lines would run. If it is connected and close to a refrigerator or kegerator, you may be able to use a small fan to keep cold air circulating (like for tap towers). Otherwise, consider a glycol system if you have the cash.
Lastly, with the difficulty in cleaning stuff that I could see, use the very best stainless steel material you can afford on anything that comes in contact with your beer.
Good luck. Post some pictures of the project. Besides myself, I bet there are plenty on here that would like to see it.