Hi Ortaç.
I am afraid this approach might not get you the answers you want. The feeling I get from your posts thus far is that you are in a position where Migrate-N could give you interesting insight into whatever you are interested in, but learning Migrate-N is not something you wish to spend much time on. That is fair enough, we all have competing priorities for our time, and we must focus on what we think is best and piques our interest. However, asking other people to do the work for you out of the goodness of their heart is probably not going to get you very far. If that is indeed the case, I think you would get a much better response if you posted a proposal for collaboration. Explain what you have, and how you think Migrate-N could help out, and ask for assistance from someone willing to collaborate --- with the understanding that if the results lead to a publication that person would be a co-author on the work. That way you get someone that has a deeper knowledge of Migrate-N to help you out directly, and you don't have to become too proficient in Migrate.
If that is not the case, and you do wish to understand Migrate more deeply, I recommend reading the manual, the associated papers in PNAS, Genetics, etc, and Peter's book chapter:
Beerli P (2009) How to use Migrate or why are Markov chain Monte Carlo programs difficult to use? In: Population genetics for animal conservation (eds Bertorelle G, Bruford M, Hauffe H, Rizzoli A, Vernesi C), pp. 42–74. Cambridge University Press, Cambridge, UK.
These should help you get a better understanding of Migrate. I would also encourage giving the tutorials on Migrate's webpage a go.
As to MCMC autocorrelation and ESS, these are diagnostics of the run. There is plenty on the web that can help you there. You can check out several good books to understand them a bit more (e.g, A First Course in Bayesian Statistical Methods
By Peter D. Hoff or Introduction to MCMC methods with R by Robert and Casella --- these provide gentle introductions to the less mathematically inclined). Darren Wilkinson's blog (
https://darrenjw.wordpress.com/) and the theoretical ecologist blog (
https://theoreticalecology.wordpress.com/) also have good resources on the topic.
Good luck.
Anders.