Extremely relevant! Check out my early work in system identification or even better to check out the work of researcher Prof. Masoud Sanayei from Tufts University.

https://link.springer.com/chapter/10.1007%2F978-0-85729-410-4_71

this may help you

Your answer is yes!

Any (by "any" I do mean all type of) modeling which needs including or incorporating a stochastic (non-deterministic) parameter can be done by MCS.

It is very promising, and compared to other methods of considering a stochastic models it is relatively easy. You do not need high level math knowledge (functional analysis and measure theory) to do MCS. They only draw back is it is computationally expensive.

Basically you have two (or three) way to approach such problems:

1- Non-destructive method (as known as MCS). Here you run your model many times and from the result you build the statistic of the result.

2- MCS enhanced with tricks (still non-destructive) like Latin Hyper-cube and Multi-Level Monte Carlo Simulation

3- Destructive Methods, here you use high level math and probability theory to study the behavior of the statistics of your model, (SPDE and SODE).

Hope it helps.

Kaveh