You don't say what you're looking for... Typical payment based on WGA minimums or non-union payment for a low budget Indie film?
Lump sums are NOT usually paid not in the actual industry i.e., Hollyweird although I have seen them happen from time to time.
How to negotiate? There are as many ways to negotiate as you can come up with... Seriously. If it were ME? I would already have a FEE AMOUNT IN MIND. The last thing you really want to do is NOT KNOW WHAT YOU'RE WORTH.
Pitfalls of an option? Tying up the screenplay for a specific amount of time. First rights of picking up the option AGAIN after the initial option runs out. Not enough money paid for the option in the first place.
How much to charge? Again, you gotta KNOW what you're worth but you can always look at WGA minimums IF you have no idea where you stand but if this is a low budget Indie film? Don't even expect anything close to WGA minimum.
Residuals are different depending on the Reuse Market the film plays in. That list is way too long to list here but you can find it here:
WGA Residuals Survival Guide
As for net points vs. investor points? Whatever you can NEGOTIATE which goes BACK to what you think you're worth. If you don't know what you're worth? I've typically seen Indie film writers earn anywhere from .5% all the way up to 10% of the film's overall budget which wasn't much. Again, whatever you can negotiate.
Typically, most prodcos will pay you a specific amount for a treatment but I've found producers wanting treatments less and less and instead opting for a first draft.
But they want something up front to see where your head is when it comes to the story you're writing. Something that tells them you're on the right track or at least something they can read and agree this story is worth telling on film.
Then there's a payment for the final draft... Final draft being based on all the notes you got from either the treatment or first draft or both if you had to submit both.
Again... There are WGA minimums for these but for a low or no budget Indie film? All this is negotiable.
I've seen writers make deals for lump sum payments. I've seen them get paid a specific amount per page... LOL. I've seen it all. Depends on what you're willing to put up with.