Is the raw data from "all" exposures routinely saved over the years? A
particular target that is observed this year, last year, 10 years ago?

In the case of the HST, I'm pretty sure you can get the raw data even
from the first images. At least semi-recent stuff is regularly re-processed
when, for instance, new algorithms for defect removal etc are implemented
or just the calibration constants improved. As computer storage is not a
big cost factor anymore, and the raw data is only a small fraction of all
the data in any case, I can't imagine anybody not archiving the raw data
"just in case".

Jan