I haven't shopped for a new door lately so I'll limit my comments--if you're correct about the stud dimension then your wall dimension (sheathing + stud + sheetrock) is going to be say, 4" instead of 4.5". Should be fine though, your door will come prehung in a jam, usually the jam will be 5.5" wide and end up flush on the inside with your sheetrock, then you apply casing trim to overlap the jam, right? In your case you could either mill a custom casing, that has a rabbet such that it is say, 1" stock, and has the rabbet cut to lap over the jam. Or, you could run casing straight up against the jam too. Would work fine, just not quite standard.
From the picture I wouldn't be surprised if you need to do a bit of carpentry under the threshold, too, it looks a bit beat up.