Most manufactured homes built in the late 80s were framed with 2x4s centred on 16 inch. You might find them on 24 inch but no less. In either event 1/2 inch sheet rock would work fine. The thicker you make the sheets the more difficult it will be to refinish around the doors and windows. The finished half inch will look exactly like the 3/8 but cost you a bit less.
Hanging the rock horizontally or vertically is up to you. I have had professional sheet rock hangers that have gone both ways in different homes that I renovated. Each method has it benefits, both look the same when finished and trimmed properly.
There is no comparison between taped and mud or bat trim on the seams. The mud finish will give your home a modern, clean, site built appearance. Trim, like all wood products, has gotten to be quiet expensive. If you have the skills to tape and mud you will be much happier with the tape/mud method.
I am in Florida and have re-plumbed about 40 manufactured homes. I have always used half inch CPVC, rather than any rolled tubing. Im not sure about the cost difference, but it is easier for me to deal with hard piping then rolling it under the home. I use the CPVC for hot and cold so I dont need to stock up on 2 different types of material. We have never had any problem doing this... as a matter of fact the half inch will result in better water pressure than the 3/4.
As far as where to run the pipe. We can just hang the plumbing under the home, below the insulation here because we have few problems with freezing. I have never put them into the walls but always followed under the original path. Drilling holes in each and every wall stud could compromise the strength of the wall. I have seen some folks run the pipes along the baseboard and case it in. I think I would rather have potential leaks under the home than in the walls or inside the home. One leaky pipe inside can cost tens of thousands of dollars in damage overnight. While it will be more difficult to open the insulation to run the new plumbing it is the best method for the long run.
If the existing water heater is doing the job and not running up your electric bill too badly why change it... If it aint broken don't fix it.
See the following free articles in our repair archives that may be helpful.
Hangin' Drywall For Beginners
Understanding and Installing Manufactured Housing Waterlines
How to select and install a heat tape
What is A Plumbing Check Vent?
Manufactured Home Ceilings - Repairing or Rebuilding
Tax Deductions For Home Improvements?
You may also want to download The Manual for Manufactured Home Repair & Upgrade This is the only book of its type, available to the public, that we have been able to find. As you would expect from the title, The repair and upgrade techniques described in this manual are specific to manufactured homes.
This book will answer almost every question on manufactured home repair that we have ever heard. Not only does this book show you how to repair and maintain your home, but also great methods for upgrading it. With "The Manual" next to your tool box you will be ready for any renovations you may decide to make.