A:
What qualifies as controversial is difficult to define. It often means that something was acceptable according to some and unacceptable in other people's view. People having different opinions is often the cause of controversy, which often occurs in cases where there is no clear rule or precedent, such as when something is new or it is at the borderline between what is considered correct and what is seen as incorrect.
Something debatable is something it is natural to discuss because there is no clear consensus on it. This can be because it is controversial, but it can also simply be because it is unknown. Actually debating such matters will often not yield significant results, because often what is actually missing is knowledge; but sometimes it does help to come together and take the time to think things through, so that a conclusion, opinion or plan can be made.
What is controversial depends on the time and place. Anything can be controversial if people differ in opinion about it, especially if they also find the issue important. One example of a current controversial topic in many countries is whether there are or ought to be multiple genders, or only two; i.e. the question of whether considering oneself to be neither male nor female is appropriate or not.
An example of something which is debatable is whether eggs are healthy. It's not especially controversial, as people tend to respect people having different opinions and making different decisions. It is debatable, though, because there's no obvious, universal answer (i.e., it is uncertain, which is the essence of what makes it debatable); exchanging views and doing research can get you someway along in figuring out whether it's true, and help create a nuanced picture by suggesting to what extent one should incorporate eggs into one's diet, and for whom it is healthy and for whom it is unhealthy.