Your question "Is the predictability of the future to whatever extent is possible (based on the present and the past) equivalent to the principle of causality?" has the trivial answer ''no'' as the qualification ''to whatever extent is possible'' turns your assumption into a tautology. The tautology makes your statement false, as your question asks whether the universally true statement is equivalent to causality. An answer "true" would make any theory causal, thus making the concept meaningless.
Why is your assumption a tautology? No matter which theory one considers, the future is always predictable to precisely the extent this is possible (based on whatever knowledge one has). In particular, this is the case even in a classical relativistic theory with tachyons or in theories where antimatter moves from the future to the past.
However, in orthodox quantum mechanics and quantum field theory, causality is related to prepareability, not to predictability.
On the quantum field theory level (from which all higher levels derive), causality means that arbitrary observable operators $A$ and $B$ constructed from the fields of the QFT at points in supports $X_A$ and $X_B$ in space-time commute whenever $X_A$ and $X_B$ are causally independent, i.e., if (x_A-x_B is spacelike for arbitrary $x_A\in X_A$ and . $x_B\in X_B$.
Loosely speaking, this is equivalent to the requirement that that, at least in principle, arbitrary observables can be independently prepared in causally independent regions.
Arguments from representation theory (almost completely presented in Volume 1 of the QFT books by Weinberg) then imply that all observable fields must realize causal unitary representations of the Poincare group, i.e., representations in which the spectrum of the momentum 4-vector is timelike or lightlike.
This excludes tachyon states. While the latter may occur as unobservable unrenormalized fields in QFTs with broken symmetry, the observable fields are causal even in this case.
This is a very interesting question. Indeed, as a one-way-speed-of-light (OWSOL) experiment the answer is a duplicate of all of the other myriad OWSOL questions: there is no possible experiment which can measure the OWSOL. However, this question is unique in that it is the only question I have ever seen that does not use light in the experiment and instead relies on relativistic kinematics to make the argument. I am not sure how to treat questions that are not duplicates with answers that are duplicates, so I will go ahead and answer.
Indeed, as you point out there is no way to measure the OWSOL, so this experiment is no exception. To measure the OWSOL it must be treated as a variable and then the equations of the experiment need to be solved to find that variable. Here, I will use Anderson's convention and use units such that the two-way speed of light is $c=1$. Anderson's $\kappa$ is related to the more famous Reichenbach $\epsilon$ by $\kappa = 2 \epsilon -1$, but I find Anderson's approach more convenient to work with. I will use lower case letters for variables in a standard Einstein synchronized frame (Minkowski metric with isotropic OWSOL) and upper case letters for variables in the Anderson synchronized frame (anisotropic OWSOL).
The transformation between the frames is: $$t=T+\kappa X$$ $$x = X$$ and the metric in the Anderson frame is $$ds^2=-dT^2+\left(1-\kappa^2 \right) dX^2-2\kappa \ dT \ dX$$
So in an Einstein frame if electron 1 is emitted with velocity $v_1$ and electron 2 is emitted with velocity $v_2$ then in the Anderson frame the velocities are $$V_1=\frac{v_1}{1-\kappa \ v_1}$$ $$V_2=\frac{v_2}{1-\kappa \ v_2}$$ Then to travel a distance $L$ requires a time $T_1=L/V_1$ and $T_2=L/V_2$. Substituting and simplifying we get $$T_1=L\left(\frac{1}{v_1}-\kappa\right)$$ $$T_2=L\left(\frac{1}{v_2}-\kappa\right)$$ $$\Delta T = T_2-T_1 = L\left(\frac{1}{v_2}-\frac{1}{v_1} \right) $$ So indeed a measurement of $\Delta T$ provides no information on $\kappa$, the OWSOL asymmetry parameter, and this experiment will yield the same answer regardless of the OWSOL.
The above analysis is a purely kinematical analysis and applies irrespective of the dynamics. Regardless of the dynamics, the experiment provides no information on the OWSOL. However, it is also instructive to delve into the dynamics regarding the energies of the electrons, since that was a key element in distinguishing Newtonian from relativistic physics.
From the metric the Lagrangian of a free massive particle in the Anderson frame is $$\mathcal{L}=m\sqrt{\dot T^2-\left(1-\kappa^2 \right) \dot X^2+2\kappa \ \dot T \ \dot X}$$ which is cyclic in $T$. This leads to a conserved total energy of $$E=m\frac{1+\kappa \ V}{\sqrt{1-\left(1-\kappa^2\right) V^2+2 \kappa \ V}}$$ So the relationship between velocity and kinetic energy is also anisotropic in the Anderson coordinates unless $\kappa=0$ and we recover the standard relativistic formula. I leave it as an exercise to the interested reader to show that the above formula for energy leads to the correct velocity in each direction shown above. However, note that the Taylor series expansion of the total energy is $$E = m + \frac{m}{2} V^2 - \kappa m V^3 + \left(\frac{3m}{8} + \frac{3m \kappa^2}{2}\right) V^4 + O(V^5)$$ which includes the rest energy $m$, the Newtonian KE $\frac{1}{2}mV^2$ and the usual lowest order relativistic energy correction term $\frac{3}{8}mV^4$. However, note that the lowest order anisotropy correction term $-\kappa m V^3$ is larger than the relativistic correction term.
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To newcomers to relativity it seems to be based on the invariance of the speed of light. While this has some historic significance, these days we regard Lorentz invariance as the fundamental principle, and a constant speed of any massless particle is then just a consequence of Lorentz invariance.
So your question could, and should, be written as the equivalent question:
And the answer is that yes indeed, Lorentz invariance has been questioned many times and continues to be questioned. Rather than attempt a review here let me just point you to the Wikipedia page on the subject.
While various speculative theories suggest there many be small violations of Lorentz invariance under extreme conditions, you should note that Lorentz invariance is at the very worst expected to be an exceedingly accurate approximation. Quantum field theory is based on Lorentz invariance and it has been tested to extremely high accuracy.