Can only one now imply every future? In logic, A implies B, if B is always true in instances where A is true. 
Obviously, there can only be one possible future, for every potential now, that is, in all instances where a certain now is true, the same future must be true. Otherwise, the flow of time would be totally unpredictable and random. But how is it the other way around, going backwards in time? Can the same future be derived from several different pasts or now, making it intractable, or is there only one now that can imply every future?
I find that if there are indeed several potential nows that can  lead to the same future, then this will eventually cause time to repeat itself in a loop. Furthermore, it will lead to a progressively conform array of timelines.
 A: 
Can only one now imply every future?

In other words, "is the mathematical model of nature deterministic", a one to one correspondence , or a one to many?.
Classical mechanics and electrodynamics are deterministic by construction. The parameters of the future solution have one to one correspondence with the parameters of the past. Thermodynamics if dependent on classical statistical mechanics in principle is deterministic, but in effect one works with probabilities because of the complexity of large numbers of constants that would determine an enormous number of trajectories , with the possible errors.
Quantum mechanics is probabilistic in nature, and mainstream physics accepts that quantum mechanics is the underlying level of all of observed natural phenomena. The equations of quantum mechanics determine probabilities, not fixed trajectories , thus from individual events detected in the future, one can only project a probability of their coming from some specific parameters of the past .

Can the same future be derived from several different pasts or now, making it intractable, or is there only one now that can imply every future?

There exists a probability that a same within measurement errors and the Heisenberg uncertainty future can come from different pasts , also bounded by measurement errors and the heisenberg uncetainty.
Since every quantum mechanical estimate is probabilistic, there is no way to generate the circularity you envisage. Only a fuzziness in the future correlated to a fuzziness in the past.
I do not see the logic of you last paragraph or agree with it, even for a classical universe:

I find that if there are indeed several potential nows that can lead to the same future, then this will eventually cause time to repeat itself in a loop. Furthermore, it will lead to a progressively conform array of timelines.

Time is a coordinate going to + infinity, what repetitions?
A: There can be many possible futures. It's a staple of standard quantum mechanics that you list all the possible futures and state the relative frequency of getting the different results.
Such a prediction is falsifiable in many ways, either by doing the experiment and getting a result that isn't on the list. Or elese doing the experiment many times and getting a relative frequencies of the different results that is very different than the relative frequencies predicted by the theory.
It's like if you rolled a dice and got a seven. That would definitely contradict the theory that you get 1, 2, 3, 4, 5, or 6 all with equal relative frequencies.
Or it would be like if you rolled a dice a trillion times and got six 99% of the time. That would definitely raise doubt against the theory that you get 1, 2, 3, 4, 5, or 6 all with equal relative frequencies.
Now even without quantum mechanics the same thing happens. A theory restricts certain observations either by outright saying they don't happen or by saying they happen at a specific frequency relative to other outcomes.
So for instance $\vec F=m\vec a$ forbids any function $\vec r(t)$ that doesn't satisfy $\vec F=m\vec a$. And if you pick a force law that allows multiple solutions to $\vec F=m\vec a$ (such as Norton's Dome) then you can still do science by proposing a theory to predict the rate you get the different results.
If different solutions to Norton's Dome predict a relative frequency for the different amounts of time it takes to go from A to B, then it allows multiple pasts when moving away from the Dome as well as multiple futures when moving towards the Dome.
