The process of turning data from astronomical instruments into measurements
useful for doing science with. It is called "reduction" because you are
usually taking large quantities of data (such as an entire image) and
turning it into one or two useful numbers (such as the brightness of
an object in the image).
The time that the "shutter" on the telescope instrument is open. The longer
the exposure time, the fainter the things that can be
seen. Exposure times on professional telescopes can be anywhere from
tiny fractions of a second for studying bright stars to many hours
when hunting for very faint objects.
The sensitivity of an instrument is
a measure of how well it detects light. More sensitive instruments
let astronomers see fainter objects and make better measurements.