For how long does vertigo persist?

It can vary. Depending on the cause it can last anywhere from seconds to hours, weeks or years. Each cause has its own time period. If you are concerned about a particular case please give more specifics.
Depends on the cause. There are many conditions that can cause dizziness and/or vertigo. Is this the result of trauma? A detailed medical history and examination are required to identify the cause. A timeframe for anticipated resolution can then be established.