black hole - Has Hawking Radiation Ever Been Observed?

According to this MIT Technology Review "First Observation of Hawking Radiation" and an associated article "Hawking radiation from ultrashort laser pulse filaments" where the authors have simulated Hawking radiation in the laboratory, using ultrashort laser pulse filaments.

So, in part answer to your question, yes Hawking Radiation is believed to have been observed, but in a laboratory environment.

According to "Observing Hawking radiation in Bose-Einstein condensates
via correlation measurements" (Fabbri, 2012), direct observation of the Hawking radiation is (in their word): hopeless.

However, once again simulations are possible:

Hawking effect, which depends only on kinematical properties of wave propagation
in the presence of horizons, is present also in nongravitational contexts,
for instance in stationary fluids undergoing supersonic flow.

From these articles, it would seem that direct observations of Hawking radiation is not feasible currently; however, we are able to produce analogues of the phenomena in the laboratory.