In some fanfictions, Damon's werewolf bite might lead to a series of events that test his relationship with Elena. For example, Elena could be desperate to find a cure for him and in the process, they discover new secrets about the supernatural world that was previously unknown. The bite could also be a catalyst for Damon to face his inner demons and re - evaluate his actions throughout his long life.
First, stay calm. Panicking will only make your heart pump faster and spread the venom more quickly. Then, try to immobilize the bitten limb. For example, if it's your leg, don't move it around a lot.
Perhaps in a fanfiction, Damon's werewolf bite is part of a grander scheme. An enemy of his arranges for him to be bitten so that they can take over Mystic Falls while Damon is weakened. Damon has to fight not only the effects of the bite but also this new threat to his home. This could involve a lot of political intrigue among the vampires, werewolves, and witches in the area.
One possible motive could be protection. Maybe Damon senses a danger approaching the reader and biting them is his way of marking them as under his protection. In the vampire world, a bite can be a sign of claiming someone.
Well, Vincent survives mainly because of his ability to adapt quickly to unexpected circumstances. Also, he has a certain level of street smarts that helps him avoid getting caught in fatal traps. Plus, maybe a bit of divine intervention or just the plot's design to keep him alive for the story to unfold.
Flash often uses his super speed and quick thinking to navigate through crises. His speed gives him the ability to react fast and find solutions that others might miss.