[Keeper of Dol Guldur]

Well, Morgoth, unlike Sauron, didn't rely in his later years on a ring to do his creating, which bound things to it. So, presumably, his "gifts" (and the mark of shadow and being burnt by the sun) lasted forever.

Sauron's werewolves were created long before he thought up rings and Barad-Dur, and Gandalf hinted that several of them were still around, within Barad-Dur. Their construction, or at least genetic tampering, wasn't done with any ring for luck and power, and they had nothing to do with it.

The same would be true of Morgoth, who had the power to make the Music of the Ainur, even if his songs were those of discord and chaos.

The powers given to his disciples were permanent.

Smaug only ever grew stronger, even after Morgoth was cast into the void. The same is true about Sauron. Durin's Bane, presumably, was stronger than before as well.

Anyway, whether it was visible or not, the Balrogs had to have solid mass. They had to be real, vile creatures, and not just phantoms of smoke and shadow. The whips were real whips (and no, Durin's Bane's whip wasn't referred to as flaming ... although I believe Feanor may have been killed by red hot lashes).

The sword of red hot metal was presumably either reflecting the red in the Balrog's eyes, or was heated by the tremendous fiery spirit of the 'Rog. If it erupted in fire at the touch, and burned Gandalf just to touch it, it seems like Balrogs are filled with red hot fire (or magma for innerds, as the movie depicted it).