I will be denoting Prime for the first introduced universe and alternate for the "Over there" Universe.
ZFT (Prime) was written by Walter (Prime) and Bell (either of them or both of them with a typewriter in Walter's lab that Bell had purchased) after the death of his son, and subsequent kidnapping of Peter in all timelines. Memory of this was then lost when Walter had sections of his brain removed. ZFT (Prime) was a warning of the future war with an Alternate Universe which is more technologically advanced and will seek the destruction of our universe. It was written to prepare for the inevitable response from Walter's alternate over the kidnap of Peter and the "breaking" of the Alternate universe.
ZFT (Alternate) was written by Secretary Bishop to cover up the true causes of the holes in their universe. Though it shared the same name name, it was not shown to be known that it was an acronym of Zerstörung durch Fortschritte der Technologie. This may have been an "inside joke" by Secretary Bishop who did know the true cause of the degradation as technological progress from the other side, but this is speculation.
In the First timeline ZFT was also an Organization that was preparing for this war. Lead by David Robert Jones he seemed to be following the plan laid down by Bell and Walter, pushing forward with Cortexiphan and other experiential research to create weapons for the war. William Bell and Nina Sharp may have been involved with ZFT at this point, with more than circumstantial evidence pointing at their involvement. However with the death of David Robert Jones and Fringe Division entering the fray against the alternate universe any assistance they may have given seems to have refocused away from ZFT and to Fringe Division.
In the Second timeline William Bell was definitely the leader of ZFT directing David Robert Jones and an alternate Nina Sharp. The stated purpose of ZFT was still to defend the world from retribution from the alternate universe for kidnapping Peter and "breaking" the universe. However Fringe Division was never able to discover ZFT or stop David Robert Jones. As such we see that the true ends of this ZFT was the destruction of both universes to create a new one as postulated by Walter and Bell after the kidnap of Peter but before Walter had parts of his brain surgically removed.
I speculate that in the First Timeline both Nina and Bell were involved in the leadership and support of ZFT. Bell's intention was always to create the new universe using the technology developed by Massive Dynamics and ZFT. That purpose was masked behind the veneer of defending from attacks by the alternate universe. With the loss of David Robert Jones before he could reconnect with Bell in the Alternate Universe, and Fringe divisions continual interference in ZFT's activities that goal became unreachable or was delayed. This forced both Bell (with his remaining lifespan left) and Nina to focus on the defense of the Prime Universe.
In the Second Timeline Fringe Division did not directly oppose ZFT and they were able to operate freely until after the Bridge Device was activated. But with Nina raising Olivia she may have become unsuitable to participate in the ZFT plan due to her attachment to Olivia and potential objections to her useage. Hence the introduction of the Alternate Nina, there may have been involvement of an Alternate Nina in the first timeline but I did not see any indication of it.