RE 2: could you please clarify your question? Perhaps provide an example of what you’d like to do? There’s nothing about Monte Carlo methods that stop you correlating parameters (although you do need to quantify the correlations); although it’s normally easier and more interpretable to instead form your model on the basis of uncorrelated input parameters then use functions of these parameters to induce correlation in the output.
RE 2: could you please clarify your question? Perhaps provide an example of what you’d like to do? There’s nothing about Monte Carlo methods that stop you correlating parameters (although you do need to quantify the correlations); although it’s normally easier and more interpretable to instead form your model on the basis of uncorrelated input parameters then use functions of these parameters to induce correlation in the output.