ANSWER:

All these Imams act as one Imam. Praying with them all till witr means that you have prayed the whole night. 

In my local masjid they switch imam every 2-4 rakah. Is this premissable? Will it also be recorded for me that I prayed the whole night behind a imam, even though i prayed behind 2 and sometimes 3 imams?

Taraweeh, Tahajjud and Qiyam-ul-Layl |