I feel really dumb asking this question, but I need help reading the lines on my tape measure. I need to make precise measurements, but given the thickness of the inch lines, I'm not sure how. I've added lines in the following picture.
I assume 1 inch is exactly the distance from the red line to the green line, or alternatively, the distance from the cyan line to the pink line. Is this accurate?
That's the wrong tool for the job.
A carpenter's tape isn't intended to do better than about 1/32" (half the width of the smallest marked interval). Taking into account the sliding hook arrangement (which accounts for its thickness), the relatively imprecise bend in the hook, and the printing quality and you simply can't do what you seek to do.
But you be the judge.
To address your final question, your assumption would have to be correct or there'd be a cumulative error in the tape measure. Left-to-left, center-to-center, and right-to-right are all correct answers to a different question than what's in your title. You can select any point on the tape and the same relative point in the following inch demarcation and you'll have an inch. The implication here is that you can "cut an inch" (or any unit) and use only the lines rather than the hook, but it still comes down to your eye (and your math skills).
The rule of thumb I've always been taught is that the line width is the inherent uncertainty of the measuring device. For example, a nice, laser etched starrett rule allows you to quite positively slot the edge of a marking knife right into the measurement - to the uncertainty of the width of that slot. The line of a measuring tape is no thicker than a pencil line, which is generally the marking tool used in conjunction.
This is, unfortunately, not a hard and fast rule but a "trick of the trade", however it generally maintains itself as cheaper measuring tools generally have thicker lines.
