On our 2001 boat the bathroom GRP mould is backed with a thick plywood bulkhead on the engine side. I see you have an inspection hatch there, so you can just open it and look if that's also the case. If so, no problem drilling and screwing on a better latch.
Would definitely add a seal to the fridge, else a lot of moist air will get in and end up as frost on the evaporator. Looks like a foam seal would work best. A compressible D or P shaped rubber profile might also work and provide a better seal, but leave the fridge lid sticking out a bit more.