If someone tries to hit a shadow created by the Project Image spell, does someone have to roll to hit? If so, does it have a low AC like a Figment, before they roll Will to disbelieve, or does it work differently?
I would say it has the same AC as the caster.
It's not a figment, so the figment AC rules don't apply. There is no general shadow AC rule - other specific spells have them, but that's not really relevant.
It's a seventh fricking level spell. A seventh level spell to make an illusion of you - I'd give the PC a hell of a lot of leeway on it. Otherwise it seems like you could do the same thing with much lower level illusion spells.
I think that I would argue that the AC is irrelevant. As with all illusions, the relevant point is whether or not the opponent recognizes it as an illusion or not, via their willpower saving throw. The rules on illusions state that when they interact with it "in some manner" they get to make the saving throw to disbelieve it. If they fail, the continue to believe it is real. It doesn't say that they have to hit it, only that they have to interact with it in some manner. I would rule that merely making the attempt to hit/attack affords the opponent that save, regardless of whether or not they might have overcome any particular AC with their attack. If they fail their save, then as a DM I would continue to act as if the foe believed in the illusion.
As a semi-related side note, the description also raises another interesting question. Since spells cast by the PC can originate from the shadow duplicate image, is a foe still affected by those spells that originate from the image?
Project image seems like a beefier version of shadow conjuration. Although mxyzplk brings up an excellent point about the level of the spell, if you don't think the projection should have the AC of the caster or can't find a more specific rule, you could use shadow conjuration's rules to stat up the projection:
A shadow creature has one-fifth the hit points of a normal creature of its kind (regardless of whether it's recognized as shadowy). It deals normal damage and has all normal abilities and weaknesses. Against a creature that recognizes it as a shadow creature, however, the shadow creature's damage is one-fifth (20%) normal, and all special abilities that do not deal lethal damage are only 20% likely to work. (Roll for each use and each affected character separately.) Furthermore, the shadow creature's AC bonuses are just one-fifth as large.