There are multiple ethical issues. Firstly, it violates the trust that students place in their professors as educators. Secondly, it can create a hostile learning environment for other students if they become aware of such a relationship. Thirdly, it goes against professional ethics codes in academia which are designed to maintain a proper and respectful educational environment.
I know a math professor who was very patient with his students. He would stay after class to help those who were struggling with the concepts. He even started an online tutoring system for his students so that they could get help at any time. His students really respected and loved him for his selfless dedication.
It depends. In some niche or more edgy forms of literature, it might be a plot point. But in mainstream movies and books, it's not overly common due to the sensitive and often unethical nature of such a relationship. However, when it does appear, it's usually used to create shock value or to make a statement about the breakdown of proper conduct in an academic setting.
Professor Snape's real story is quite a journey. He was a brilliant potions master, but his character was much more than that. His relationship with the Marauders in his youth was also a part of his story. They bullied him, which added to his bitterness. But his true heroism lies in his long - term plan to bring down Voldemort. He used his position as a Death Eater - turned - spy to pass on crucial information. His story is a testament to how appearances can be deceiving, as most people only saw the harsh and unlikable side of him, not realizing his noble intentions.
Professor Snape's real story is one of a complex and often misunderstood character. He was a double agent in the wizarding world. He was initially seen as a villain, especially by Harry Potter and his friends. But in reality, he was deeply in love with Lily Potter and his actions were often driven by his love for her and his desire to protect her son, Harry, from Voldemort.
If 'Professor Proton' is from a particular TV show or movie, more context is needed. However, generally speaking, if he is a fictional professor character, his real story would be the backstory created by the writers. It might involve his education, his research interests, and his relationships with other characters in that fictional world.
I'm not entirely sure specifically about a 'Professor Hogg' in 'The Crown' as it may be a relatively minor or specific plot point. It could be a fictional character created to serve a particular storyline within the context of the show, perhaps related to academic or political storylines that are common in 'The Crown'.