The One Ring can corrupt its wearer and make them invisible (potentially with other powers?), but I'm unsure what the other rings of power could do. Were they only able to make the Nazgûl immortal, or did they have other powers?
The Simarillion says that the men who were granted the rings obtained "power" and became "sorcerers" (thus, the "Witch-King") but we don't get too much in the way of specifics.
Those who used the Nine Rings became mighty in their day, kings, sorcerers, and warriors of old. They obtained glory and great wealth, yet it turned to their undoing. They had, as it seemed, unending life, yet life became unendurable to them. They could walk, if they would, unseen by all eyes in this world beneath the sun, and they could see things in worlds invisible to mortal men; but too often they beheld only the phantoms and delusions of Sauron. And one by one, sooner or later, according to their native strength and to the good or evil of their wills in the beginning, they fell under the thraldom of the ring that they bore and of the domination of the One which was Sauron's. And they became forever invisible save to him that wore the Ruling Ring, and they entered into the realm of shadows. The Nazgûl were they, the Ringwraiths, the Úlairi, the Enemy's most terrible servants; darkness went with them, and they cried with the voices of death.
So other than the powers you listed, the two major other ones would be invisibility—and first at will, and then permanently—and some sort of visionary power.
Another I would add from the Lord of the Rings would be their piercing screams, which are said to strike terror in the hearts of ordinary men. There's also a lot in The Lord of the Rings suggesting the wraiths have the power to strike fear in those around them, but it's not clear if that's a magical power or if they're just very intimidating—magic in Tolkein's universe tends to be very subtle.
Somewhat less subtly, we do at one point see the Witch-King casting a spell to set his sword on fire:
The Black Rider flung back his hood, and behold! he had a kingly crown; and yet upon no head visible was it set. The red fires shone between it and the mantled shoulders vast and dark. From a mouth unseen there came a deadly laughter. ‘Old fool!’ he said. ‘Old fool! This is my hour. Do you not know Death when you see it? Die now and curse in vain!’ And with that he lifted high his sword and flames ran down the blade.