I've heard that praying Taraweeh behind the imam and the Witr also is like praying the whole night, could you please be kind enough to verify this for me?

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is proved in a Hadith that the Prophet said: "Whoever performs the night prayer with an Imam until the latter leaves, he is given the reward of a whole night". [Reported in the four books of Sunan with a sound chain]
No doubt that Taraweeh is from the night prayers. So if one prays with Imam until the Imam finishes his prayer he will get the reward of praying the whole night.
Allah knows best.