Albeit rather late I would like to add the following reference as another answer to your question (1): dimensional regularization was is also treated rigorously in

P. Etingof, *Note on Dimensional Regularization* in Vol 1, pp 597–607, of [Quantum Fields and Strings: A Course for Mathematicians](http://bookstore.ams.org/qft-1-2-s) (see also [here](http://www.math.ias.edu/QFT/fall/index.html)).