Are there any known children of Hades (god or mortal)?
If there are any mortal children of Hades, would they have abilities related to spirits and souls?
Yes, and for future questions of this type, Theoi is a great resource.
Depending on the source, he had three children plus the Erinyes. The latter are problematic, as Aeschylus' Oresteia presume their primordial, pre-Olympian existence.
Zagreus was also said to be the son of Zeus and Persephone (as related in an Orphic hymn and then later authors). This is probably secondary, though, and doesn't really jibe with the very early Hymn to Demeter, where Persephone is a young maiden before she is taken away by Hades—when would Zeus have had a chance?
Melinoe was actually the child of Zeus, but Zeus had taken on the form of Hades, so take that as you will.
Nothing contests Makaria's parentage, but the Suidas is very late (10th century AD, so well into the Middle Ages already) and often full of inaccuracies, so we have no idea how early or late or even correct the attribution is.