It is correct that hawking radiation is virtual particles that turn into real particles, when matter falls in (or anti-matter) it well send out em-radiation, you know x-rays or gamma rays (incidentaly alpha rays are helium nucleus`s and beta rays are high energy electrons). Black holes will also like you said tear positron-electron partners apart and that is detectable as radiation, 1: beta rays and 2: because electrons recieve and give of photons every time the make a "quatum jump" or "quantum leap". I hope this answers some of your questions.
(virtual particles are actually things like photons, gravitons, gluons etc.. they fall under the name of bosons, they are only detectable by the force they exert when they get real we can actually see them like fermions, quarks, electrons, neutrons, protons etc...)