Is all sausage considered a "Processed Meat"?
Generally it's things that have been prepared such that there's some sort of added preservative -- salt, sulfates, sulfides, nitrates, etc.  So this would include all hams except 'fresh ham', almost all deli meats, all sausages, bacon, jerky, corned beef, etc.

So yes, sausage is considered a processed meat.

If you want to get all technical about what 'processed' means it could also include any other form of curing (eg, smoking), and most any form of processing (grinding, slicing, etc), although this second group typically isn't refered to as 'processed meat' (unless it's then glued back together, like chicken nuggets, but those tend to have additives in them already)

As for the health aspects ... like most anything, it's fine in moderation, although there are some people who react badly to sulfates and sulfides.  Some sausages have more additives in them than others, and there are plenty of sausages out there that might be considered 'healthy' if it's in place of other higher salt/fat foods (eg, some brands of chicken &amp; apple sausage).