It's evident that this method is better suited for setting a lower limit on the age, given all the standard physics assumptions, than an upper limit.
Absolutely. That's exactly what it represents: a lower bound on the age of the Universe.
As to whether they found the faintest white Dwarf, they will get answer to that when they use the new Hubble camera, which is vastly more sensitive that the one used for this study.
Given that universal expansion is accelerating, it's difficult to determine how much of the universal expansion is due to initial conditions (ballistics of the "big bang") and how much is due to a continual expansion of empty space itself. It could have been a "big whoosh" instead, perhaps. To extrapolate everything back to a "small" point may be possible, but what science can say about the nature and history of things around that point is more severely limited than some scientists seem willing to admit. It is not possible to create (or find) and make measurement on objects that even remotely approach such conditions, by many, many degrees of magnitude.
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