Does divorce occur by threat, or if one swears by divorce and the wife does what was sworn upon, or if one utters it in a state of extreme anger? Are these divorces counted? Is a Shaykh or a Ma'dhun required for reconciliation?

To begin with, anger is a blameworthy trait that harms both one's religious and worldly affairs. As for your statement to your wife, "If you do such and such, you are divorced," if you intended to make the divorce contingent on her doing these things, then it is a conditional divorce that takes effect, according to the majority of scholars, upon the occurrence of the condition. A divorce counts each time the condition you set occurs. However, if you merely intended to threaten her with divorce, then nothing results from it unless you actually carry out your threat and pronounce the divorce. As for the two times you explicitly pronounced divorce, they have undoubtedly occurred, and anger does not prevent the occurrence of divorce except in specific cases. You should consult scholars or a Sharia (definition) court to assess the extent to which anger affects the occurrence of divorce.