To deal with the questions in a different order:
1. Yes, the definition of absorbance in an HPLC detector is the same as in a spectrophootometer. In fact, a UV detector is essentially a dedicated spectrophotometer with a flow cell.
2. The discussion about linear range stems from the fact that an absorbance detector does not *measure* absorbance; it measures transmittance (the fraction of the incident light that gets trough the cell) and the calculates absorbance (it's the negative log of the transmittance). The problem is that any spectrophotomer will see a certain amount of "stray light". Imagine for a moment the situation where the flow cell is perfectly opaque (the sample has effectively zero trasmittance). If the stray light was 1% of the incident light, the detector would never report transmittance less than 0.01 -- which is 2 absorbance units, and the response would start to become non-linear somewhere around 1.5 or a bit less.
This is a long-winded way of explaining why "maximum" absorbance values differ: they depend on how much non-linearity you can tolerate and on how much stray light the detector design allows.
3. The detector is an electronic instrument. Its output signal is actually a *voltage* that is proportional to the absorbance. The proportionality is commonly (but not always) 1V = 1AU; on some detectors it is switchable either in software or via a physical switch. Because quantitation in chromatography is inherently a *comparative* process, it really doesn't matter which units are used so long as the calibrators and samples use the *same* units.