It looks to be old coffee residue. Most likely never cleaned, so the coffee oils and residue collected and caked on over the years.
I do not believe it is rust.
I would start with these tools whether you take it all apart or not.
A lot of time and elbow grease. IMO I would start with the putty knife and take off as much of the heavy residue as possible.
Then the hand held steel brush and razor blade.The brush bit for the drill would be my last resort applying light pressure carefully.
I would also mix a little white vinegar with warm water solution, apply to cloth to clean. Then wipe it down with a a damp cloth
soaked with hot water. I have taken apart a lot of electric burr grinders and espresso grinders for deep cleaning. Not a fun
job, but as you can see necessary. when you are finished cleaning, put a little bit of white rice in to grind before coffee. Since it is not electric,
you might want to be cranking the handle while some one else can drop in a little rice at a time, so it does not clog. Does a nice job
for finishing up. Hope this helps a little.