How does the 0.01% look in comparison to the natural variability of star brightness, due to cycles, spots etc? Would that be a concern in terms of false positives? And also, given the specific line-up needed for us to see the pass, how likely it is for us to be able to observe the same planet in front of the star in the following years?
Stars do change their brightness in various other ways, but the light curve of planetary transit has a very characteristic shape. It causes the brightness to dim by a small but constant amount, with a (comparatively) very short and sharp start and end. A transit causes this pattern to occur at precisely regular intervals, and I don't think we know of any phenomena related to a star itself that would imitate the same effect.
Stars' relative positions generally don't change fast enough for the angle from which we observe a transit to change significantly. A transit of HD 20794 d is visible anywhere within a roughly 0.7-degree wide band. But our angular rate of motion with respect to the star HD 20794 is the same as its rate of motion in our sky, about 0.001 degrees per year. So the transit will most likely continue to be observable for decades or centuries to come, depending on exactly how the planet's orbit is aligned.
Would it be feasible to place telescopes at other orbital inclinations with respect to the sun in order to spot transits in stars that aren't within Earth's orbital plane ?
The orbital inclination relative to our sun doesn't really have anything to do with it. In fact, stars that are aligned with Earth's orbit are harder to observe, because they go behind the sun once a year.
Detecting an extrasolar planetary transit requires us to be aligned with the planet's orbit around its star. And since those stars are so far away, you would have to travel an immense distance away from our solar system to appreciably change the relative angle.
HD 20794 is about 20 light-years away from us, so changing our observation angle relative to it by 1 degree would require traveling about 0.35 lightyears. Our fastest-ever interstellar probe, Voyager 1, would take 5000 years to travel that distance.
Thanks for the clarification. You are absolutely right, in my post above I accidentally used the word "parallel" that caused the confusion. It wouldn't even be practically possible to use PLATO to observe them.
