Can a black dwarf be suitable for manned exploration, once it cools down? And potentially used for space mining?
A 1 solar mass, Earth sized black dwarf would have a surface gravity of about 360 000 g which probably rules out manned exploration by anything we would normally think of as human. For similar reasons, mining would be quite challenging.
Another obstacle is that the Universe is not old enough to have produced any black dwarves yet. The oldest white dwarves still have a surface temperature of thousands of Kelvins.
Indeed, if humanity is still around when they have formed, visiting and mining them will probably be easy.