How long does the input signal have to be for the device to detect the input? 

The signal duration has to be at least 50ms for the device to sense the input for 2nd generation devices. 

How does FaceStation 2 detect the input?

TTL input of FaceStation 2 is a edge detect type. If there is a level change from 0 -> 1 or 1 -> 0 it will detect the input when there is a signal change of 70% or above. 

My fire alarm panel provides a wet contact (flowing voltage) which is constantly triggering the input of a Suprema device how can I fix this? 

You should use dry contact for device inputs. If you connect a wet contact to the Suprema device, it may damage the device. 

If your input providing panel can only provide wet contact, consider using another accessory between the panel and Suprema device like below: 

Alarm Panel > relay accessory > Suprema device. For a sample relay accessory refer to the attachment.