May a man talk with his divorced wife?
No. A divorced couple may not talk to each other face to face (to the extent that even if they have a Din Torah together they may not appear together in Beis Din, but must send an agent to represent them).
However, to talk on the phone about matters in a manner that will not give cause for concern that they will become too close is permitted (such as discussing arrangements for the children etc.)
With regard to place of residence, Chazal forbade a divorced couple from living in the same building or neighborhood. However, they permitted this under certain circumstances, and every such circumstance should be referred to a competent Rav for a definitive ruling.