Well, unlike other speedsters, Savitar seems to be able to appear as mirages of dead loved ones to people. I would imagine this is part of his "you tap into the speed force, I control it" or whatever he said line.
The speed force has shown the ability to appear as images of loved ones to Barry, so if that's the case, perhaps Savitar uses that to his own maniacal ends.
His appearance is likely a speed force generated costume, so that's a new ability shown off on the series.
He's got some ties to the philosopher stone. I wonder if there's a chance he uses magic to enhance his abilities, and the stone is like his idol.