I’m not sure what directly causes (1) but I think there could be reasons behind (2)
(2) Did you create any cuda tensors before moving your model to the GPU? If not, then my handwavy explanation for this is that the moment you create a cuda tensor (e.g., directly declaring one or by moving your model to cuda), this does a whole bunch of things like spin up a cuda context and load a bunch of extra library code corresponding to GPU kernels and all of these things will take up memory.