One common theme could be mystery. Since Twilight often has an air of mystery, fanfics might play on that by having Professor Ward get involved in solving some mystery related to Twilight's world. For example, something about the origin of Twilight's powers.
Well, one great source to find 'Professor Ward Twilight' fanfics is Archive of Our Own (AO3). Just search for 'Professor Ward Twilight' there, and you'll get a list of fanfics. Some might focus on the relationship between the characters in unique ways, like exploring their backstories together or creating new adventures for them.
One common theme is the exploration of different relationships. For example, fanfics often expand on the relationships between the vampires and the werewolves. Another theme is the alteration of character destinies. Writers like to play with the idea of what would happen if a character made a different choice.
One common theme is self - discovery. Harry, in the role of the Defense Professor, often discovers new aspects of himself. Another theme is mentorship. He has to mentor the students, which is a big part of these fanfics.
In 'Caged Twilight' fanfics, a frequent theme is the transformation of characters. This could be in terms of their personalities, their abilities, or their outlooks on life. Also, the theme of mystery often pops up. The 'caged' part of the title might imply that there are secrets or hidden aspects within the story that the fanfics explore. Additionally, themes of hope and despair are also common as characters deal with their situations in the 'Caged Twilight' world.
Protection is also a theme. In some fanfics, Sinistra uses her skills and knowledge to protect Hogwarts or the students. Given that astronomy can be used for divination and predicting events, she might foresee a danger and take steps to safeguard the school. This shows her as a more proactive and important character within the Hogwarts faculty.
One common theme is the relationship between Ward and Skye. It could be exploring their romantic relationship, either in a canon - compliant way or in an alternate universe where things turned out differently for them.
Power is also a common theme. In 'Harry Potter', there are different levels of magical power and the struggle for power among the characters. In 'Twilight', the vampires have their own power hierarchies. Fanfics may combine these power dynamics, showing how characters from both series might compete or cooperate based on their power levels. Additionally, the theme of identity is often explored. Characters in both series are trying to figure out who they are. Fanfics can take this further by making characters from 'Twilight' question their identity in the wizarding world and vice versa.
Themes in 'Mistaken Vows' Twilight fanfics can vary, but often include the idea of fate and free will. A mistaken vow might seem like a twist of fate, but the characters then have to use their free will to deal with the situation. Additionally, trust is a big theme. When a vow is made in error, it can shatter the trust between characters. This then becomes a central part of the story as the characters try to either regain that trust or find new relationships based on new vows or understandings.
One common theme is the exploration of deeper emotions. Since 'Turning Page' often implies a new chapter or a new perspective, fanfics may focus on characters' inner thoughts and feelings more intensely. For example, how Edward really copes with his eternal existence in a new situation.
Unrequited love is a very common theme. Jacob loves Bella deeply, but she has feelings for Edward too. Heartbreak and betrayal also often come up. Sometimes the werewolf pack might seem to betray Jacob's trust in the context of his hurt. Another theme is isolation. Jacob may feel alone in his pain, separated from both the humans and the werewolves at times.