After cold drawing, rolling or heavy forming, when the material has work-hardened to the point where further deformation will crack it. Before machining, when a hard or uneven structure would destroy tooling or refuse to hold a finish. And after welding or a previous treatment has left a structure that will not behave predictably.
The distinction between annealing and normalising is the cooling rate. Annealing cools slowly, usually in the furnace, which produces the softest and most ductile result. Normalising cools in still air and gives a finer, slightly harder structure. If you are unsure which the drawing intends, send it and we will read it with you.
Annealing runs across both furnace types, so batch size is rarely the limiting factor. Long sections go into the six-metre gas-fired boxes; deep or awkward work goes into the electric pit furnaces, which take a metre and a half of vertical section.

Annealing goes above the critical temperature and changes the structure, softening the material. Stress relieving stays below it and releases locked-in stress without softening the part.
Slow cooling makes it one of the longer cycles, typically the better part of a working day for a standard charge. We confirm turnaround at the point of enquiry.
Yes, and it is a common reason for sending work. Welding leaves both a hardened heat-affected zone and residual stress; annealing addresses the structure, stress relieving addresses the stress alone.