Hi and welcome
The black membrane on the bottom of the floor joists is the very bottom of the camper. The water pipes would be above it, not below. If you go under the camper and look up, you will see the black membrane. That’s the same membrane you see from the top side looking down.
While the membrane can be repaired if cut, I’m not seeing how cutting it is going to help sort out where the leaks came from. If you must slit it, go under the camper and feel for a floor joist. Slit the membrane on the center of the joist. This allows a better repair to seal it back up as you can press on the joist to set the correct repair tape called Flexmend.
There are also waste water holding tanks under the floor. The black tank is right under the toilet. The black membrane is on top of the tank between the tank and bottom of the floor joist. So careful to not cut into the tank.
There is also a gray water tank. I do not know exactly where that is on your floor plan. Drain pipes from the kitchen sink will run to it. The shower and bath sink drain may be piped to the tank also if the tank is not under the bath room
To help find a fresh water line or water heater leak, if you have a small compressor pump up the water system to about 15 psi and look and listen for a leaks. The system normally runs at 50psi water pressure. If you have an active leak the 15psi should find it. You can pump air in the city water hose fitting on the side of of the camper. Not the fresh tank fill but the garden hose fitting looking one we call the city water connection.
Hope this helps
Current Sunlines: 2004 T310SR, 2004 T1950, 2004 T2475, 2007 T2499, 2004 T317SR
Prior Sunlines: 2004 T2499 - Fern Blue
2005 Ford F350 Lariat, 6.8L V10 W/ 4.10 rear axle, CC, Short Bed, SRW. Reese HP trunnion bar hitch W/ HP DC
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