Is Hawking radiation detectable? Could Hawking radiation be detected with instruments available today? If not, what sort of instruments would be required to observe it? Would there be any way to confirm through observations the existence of Hawking radiation?

I'm primarily asking about techniques that we could reasonably implement with current technology or something that could be implemented in the near future, but if you need to get close to a black hole to be able to observe the radiation and couldn't do it from a spacecraft in Earth or solar orbit, then that would be the answer.
No. Problems:


Hawking radiation would have very small temperature of $10^{-6} M_{sun}/M_{BH}$ Kelvins. Primordial black holes below 1kg already did evaporate, so there would be no sources from small black holes. The only hope is artificial black holes created by CERN.
Falling matter inside black hole would expirience enormous amount of acceleration leading to emittance of photons (particularly X-rays). So you would first are required to cut out this noise.
Black holes are surrounded by ergosphere consisting of hot plasma, which effectively blocks all photons below some critical temperature. For example, we have our radiowaves blocked in the same way by ionosphere of Earth.
(Reasons above were not enough?) There is other quantum-mechanical mechanisms of creating particle-antiparticle pairs which potentially lead to heavy emittance of antiparticles, mostly positrons from black holes. So you would somehow need to shield from positrons, and the photons coming after $e+e^{+}\rightarrow \gamma + \gamma$ kind of reactions.


You would be required somehow prepare black hole for investigation by removal surrounding physical layers from ergosphere, stopping its rotation (really impossible?). I don't know of any "surgical" instruments available today for such task ("surgical" in a sense that we will need to modify our black hole).

Our measuring instruments are totally capable, though. We also know where black holes are located. Tiny problem of communication still persists. But I think scientists would be perfectly fine to wait few millions of years for station to return. Also there is problem from the field of mechanics. It is enormously hard to cross ways with gravitationally strong object, because your trajectory (hyperbolic type) would intersect with a lot of other trajectories (of elliptic type). But I did not list it, counting on humankind getting smarter with this kind of things in a few centuries.