> When the sample absorbs IR radiation, and gets promoted to a higher vibrational energy level, does it then re-emit the photon it absorbed as in UV-vis and atomic emission spec, or is the energy simply used up?
No, IR excites vibrational energy levels (think: guitar string periodic vibrations). Energy is dissipated via non-radiative paths
> What influences the shape of the absorption bands (i.e. the sharpness/broadness thereof)? For instance, why is the O-H (alcohol) band broad, and the O-H (acid) band even broader?
This is to do with the number of Boltzmann states available in a particular solvent. Bonds to "loosely-held" hydrogens (particularly on electronegative atoms) tend to be more flexible, and thus have vibrational states across a wider range of energies, giving a broad peak.
> How exactly is the IR spectrum generated? The schematic diagram in the textbook shows a monochromator interposed between the sample and the infrared detector, suggesting the selection and detection of SINGLE wavelengths. But we all know that the IR spectrum is continuous, and shows transmission of light from around 500/cm to 4000/cm...
We make thousands of single measurements at different wavelengths, thus compiling a graph. This process takes about 10~30 seconds on a modern machine. There are more fancy methods such as Fourier Transform IR, which only require a single measurement to capture the entire spectrum, but the theory for that is way way past VCE.