1. My instincts say to space the levels to include equal areas of the Gaussian curve.
2. It would probably be easier to convert to absolute level, add, and then convert back to your nonlinear levels.
3. you could probably make a lookup table to convert to the new steps of the data. This would be a nonlinear function. This would be faster than converting back to linear, multiply, and reconvert to nonlinear.
"Vector Quantization and Signal Compression" by Allen Gersho, Robert M. Gray
Ch.5 - Scalar Quantization I : Structure and Performance
Ch.6 - Scalar Quantization II: Optimality and Design