what exactly is the Bagua stepping method and Xingyi leg and waist methods, How do they work, What are their characteristics and how are they employed in sun style taijiquan?

I think you haven't received an answer because your question is so large. You might want to read the articles on the Shenwu website about Bagua, Xingyi, and Taiji; then check another source (Emptyflower has a lot of this sort of info). Look at clips of each style. Then bring back smaller questions.

Please be aware that there is a lot of variation among even really good practitioners of each art. The only true universals seem to be the use of the follow-step in Xingyi and Sun style Taiji, and the use of the waist in all three. You may not get a good answer about HOW the waist is used because it is usually taught by feel rather than verbally described.

Bill