Open Orthodoxy is trying to push modern day societal norms and political correctness into an “Orthodox” environment even if it runs counter to halachah or accepted minhag.
As an example, a recent ruling allows a woman to nurse a baby in shul while davening.
1) Do people actually affiliate themselves with OO?
Yes
2) Is it an obvious thing (like perhaps as someone would be able to tell who is Chassidish, Yeshivish, or MO based on appearance, shuls, or hashkafah)?
Yes and no. They are mainly affiliated with a Yeshiva and Shul in Riverdale (Bronx, NY)
3) What’s the difference between MO and OO?
Modern Orthodox is a term generally used for what was once called “middle of the road”. Frum but not yeshivish. What I would call those affiliated with the Young Israel movement or Yeshiva University. (I know this may not be a fair statement.)