Age of a black hole Is there a way to measure the age of a black hole by find Hawking radiation or calculating the stable orbits around the black hole?
 A: No.  The No-hair theorem tells us that an isolated black hole is completely described by its mass, angular momentum, and net electric charge.  In fact, the charge is expected to be basically zero, so it's basically just the mass and angular momentum.  Hawking radiation and orbits only depend on those parameters as well, so they wouldn't tell us any extra information.
For realistic astrophysical black holes, there could be indirect evidence that gives us some hints, though.  For example, if the black hole was formed as a result of a supernova, it may be possible to observe evidence of the time since that supernova.  There are numerous examples of supernova remnants that can be directly imaged.  If you analyze those images — especially multiple images taken over a period of many years — you could figure out when the supernovae occurred, thus suggesting when the corresponding black hole may have formed.  (Though maybe the supernova was triggered by interaction with an existing black hole...)
There are other scenarios that I can imagine might be able to give us some hints about how long a black hole has been hanging around influencing nearby matter.  In principle, you might also be able to say something about the statistics of a population of black holes.  But indirect evidence of these sorts are really the only possibilities in accepted physics.  A black hole on its own gives us no hint about its age.
A: No. It is the nature of a black hole that its history (and age) are inaccessible to us.
A: No. The Hawking radiation could tell us the black hole's remaining lifetime, or equivalently how much mass it has. But that doesn't tell us anything of the following (which are all equivalent): how much mass it's shed; how much it once had; how long it's existed for. The argument for orbital details is analogous.
