one thing I would change is Parasite's appearance. does he have to be purple?
Kind of, yeah. It's how he's looked since the 60's. Why change it for a movie? Superman fights monsters and aliens, so there's no reason why the Parasite shouldn't look the part. The Hulk is green, Ra's Al Ghul has wacky facial hair, and the Parasite is purple. That's just the way they are, and, out of context, all those examples can
easily be pretty laughable in appearance, but I think it depends entirely on how the character is written and how the actor carries himself. I mean, despite being green, the big fight at the end of The Incredible Hulk was intense as hell and nobody was questioning the color of the Hulk's skin.
If Rudy is just standing there, full of himself but not really doing anything to paint himself in a threatening light, like this:
...then I can see how people on the streets of Metropolis wouldn't take him seriously (until he kills them, of course).
But if we see him in sinister contexts, like these...
...then I don't see how his purple skin would be a problem. It's one of the main things that the Parasite is known for. No need to change it. Ask anyone who he is, and the barest description you'll likely get is "he's the big purple guy who drains Superman's powers." DC tried changing his color to green in the 80's, and it didn't go over too well, so they changed him back to purple before too long.
and that white harness of his has to make sense as to how it gets on him and why he has it unlike in S:TAS where Rudy gets the gunk on him and the white harness comes out of nowhere.
Unlike the purple skin, Rudy doesn't need the white stripes to be recognizable. He's had a number of different looks over the years, so there's no need to adhere to a single one, or why they shouldn't feel free to take some liberties. Maybe just give him some green camouflage pants or something like that.