According to the article of Hauser:
The Hironaka theorem on resolution of singularities http://www.ams.org/journals/bull/2003-40-03/S0273-0979-03-00982-0/home.html
The existence of resolution of complex analytic varieties was proven in:
Aroca, J.-M., Hironaka, H., Vicente, J.-L.: The theory of the maximal contact. Memorias Mat. Inst. Jorge Juan, Madrid 29 (1975).
Aroca, J.-M., Hironaka, H., Vicente, J.-L.: Desingularization theorems. Memorias Mat. Inst. Jorge Juan, Madrid 29 (1975).
Question 1. I would like to know if since then some alternative more simple proofs were found? And especially are there some (relatively) recent books, lecture notes or exposition articles covering this topic?
The result of Hironaka on resolution of algebraic varieties is now exposed pedagogically in the book of Kollar: "Lectures on resolution of singularities", but as far as I can judge (please correct me if I am wrong), Kollar does not treat the case of complex analytic varieties.
Question 2. Suppose I want to use this result on resolution of singularities of complex analytic varieties (and the answer to question 1 is NO). Should I cite these two articles, or cite nothing, pretending that everyone is aware of these two aricles? I have an impression that nowadays people tend not to cite these results on resolution unless they work exactly on this problem.