How can one fix the different parameters in the geostatistical analyst tool for various interpolation techniques? such as power for IDW, Smoothening parameters for RBF, range ,sill and nugget for kriging.

Is there any range for these parameters? Should trend, transformations necessary to be considered?

Is there any range for these parameters? Should trend, transformations necessary to be considered?

Global Polynomial Interpolation, Local Polynomial Interpolation, and Kernel Smoothing are all based on polynomials, so the Order of Polynomial means the same thing in each tool. Additionally, LPI and KS share Kernel types because they're based on local kernels.

The only parameters that are shared across the board are related to the searching neighborhood (except when you introduce barriers).

The domain of each parameter depends on what the parameter does (for example, the range in kriging has to be greater than 0). These domains are all documented, and if you try to use a value outside that domain, the software will throw an error telling you that it is outside the parameter domain.

You should always consider trend removal and transformations, but that doesn't mean you have to use them. Only use them if they help create a better model (which you can judge with crossvalidation statistics).