Did the Team let Nick live after he killed Nathan?
Yes, mainly because you'll remember that there was a team arriving just as Zev and Sasha left? They had learne about the infiltration and were planning to enter Thana, thinking Nick had been kidnapped. When he ran into them, Nick convinced everyone that Zev was the one who killed Nathan and that he had held Nick at gunpoint and made him take them to the Gateaway.
Those in power mostly believed him, but were never certain. And with Zev gone permanently, Nick decided it was time for Plan B. He disappeared (he'd always held aside money and resources in case he needed to disappear.) He's in his own personal version of the witness protection program…
Will the experiments end with Nathan dead and Zev/Zan/Sasha gone?