"my getting married" - possessive pronouns replacing pronouns

I have a question about using possessive pronouns in place of regular pronouns, for example: "The probability of my getting married within the near future is slim." This was written in a textbook but a student had crossed out the "my" and wrote "me." Is the book incorrect? As another example: "Horwitz explains that certain trade agreements such as NAFTA aren’t doing enough to facilitate free trade because of their maintaining a 'heavy dose of regulation.'"

As an aside, I was always taught that when writing a paper of some sort you should put 2 spaces (from the spacebar) in between sentences but lately I've seen many people using only 1 space. What gives?