The Father of the Rhinemaidens is a Time Lord
- He told his daughters to guard the Rhinegold, which is really Time Lord technology. The Ring could be created from the living metal Validium. The Tarnhelm seems to have TARDIS technology, shapeshifting, invisbility, and teleportation. Then Siegfried can understand birds and hear Mime's thoughts after tasting Fafnir's blood. Perhaps this is from Fafnir's years of exposure to the Tarnhelm, translation units and telepathy. Prophecies can be performed due to time travel, the idea of ruling the world could have come from looking into alternate timelines. Or what the Time Lord said could have been a stable time loop to destroy the Gods.
Erda is mother of the Rhinemaidens
- Consider her other daughters, 3 Norns and 9 Valkyries, 3 Rhinemaidens seems to fit. If the Rhine is the Rhinemaiden's Father, the Earth being their Mother would fit.
There are other giants... but Fafner slew them
- That would explain why he calls himself last of the Giants. He killed them when they tried to take the ring.
The Neidings were acting for Fricka
- Who was angry at Wotan's infidelities so sent them to destroy the Walsung clan.