How is the mind matter process described and explained according to the Buddhist teachings? How does it related to Cognitive Psychology? How is the next moment created from the current? What is the mechanism behind it? How does this process sustain its self? What are the variation with regard to this if any?
Cognitive Process in Buddhism: Paticca-samuppada
Modern Science: Mental Modules come close to what the Buddha described. It was one of the topics in Robert Wright's course mentioned above.
As for your second question, the relation between the Buddhist teaching and cognitive psychology is a topic researched by Robert Wright and presented in this course: https://www.coursera.org/course/psychbuddhism