sebastian, this room would be built, except for the door, much like a custom shower stall. If a hose burst, the idea would be to limit the water damage to the wall board or plaster in the room. Its not an inexpensive room to build.
The pan idea can be worked with just fine, but understand there is a bit of risk involved with it. Its just not meant to catch all the water from a burst hose. Using the other components, like the auto-shut off, the moisture alarm, and changing out the hoses will be the most economical way to go with good coverage for problems, but not the best.
Best you can do is to build this room like a giant shower stall. A regular door, even a hollow core would be find as it will take water spraying on it directly for a period of time, but regular drywall with nothing behind it will not.
A trap primer is a device that puts a small amount of water into the drain in the floor. It does this to recharge the water seal. If it didn't, the water would dry up and the room would smell of flatulance and allow sewer gasses into the home. This device keeps the seal 'primed' all the time, automatically.
The rubber membrane would be under your drywall. The point would not for it to be completely waterproof, but to deflect the water down to the floor to go out the drain if the dry wall material failed in case of a burst hose. You would not see it in the finished room.
You can see the web page for this roll-in shower receptor here
This is a bit small, but a faux marble fabrcator in your area can make one large enough for your needs.
This is what a regualr "washer pan" looks like.
If the water doesn't come straight down on this pan, at a slow enough rate for the small drain to handle it, its useless at best. A sheet metal shop can make you a larger one that will work better than these things.