I have just a little more time this morning for a better answer, but I still don’t have enough time to give you well-written answers or look them up myself to make sure my definition matches others. Many of the terms you’ve listed are jargon, and jargon differs from one region to another and even from one shop to another. Another thing to consider is that your instructor isn’t necessarily up on most of these things either or has his or her own definition that he thinks is more widespread than it really is (trust me, design instructors don’t know everything).
Analogue proof: A hard-copy proof as opposed to a digital proof, although I’ve never heard it called analogue before
Beating: There’s a process in the manufacture of paper pulp that’s called beating. You’ll need to look it up for details. Or maybe it’s what happens to a pressman when he screws up a job.
Digesting: I’ve heard this term used in dozens of ways. I have no idea which one your instructor wants.
Dye-line: Irregular cuts are sometimes needed. A die line is supplied to the printer to guide them in making those cuts. Again, look it up (using the correct spelling).
Flatbed-cutters: There are lots of these kinds of things that do various kinds of cutting. It’s an easy one to Google.
Grippers: When paper goes through a press, things called grippers hold the edges to keep the paper in place and guide it through the press.
H&J: Hyphenate and justify, maybe. I’ve never heard anyone say H&J, though.
Hemp: Huh? Maybe your instructor is referring to paper made from hemp. Maybe your instructor has a substance abuse problem. Who knows?
ISO: International Organization of Standards. This group sets all kinds of standards for things — print-related things being one of them
Mechanical fastening: Who knows? Anything mechanical that fastens something to something else might fit this definition. Again, maybe your instructor has something specific in mind.
OCR: Optical Character Reader. It’s software that recognizes scanned letter shapes and converts it into text.
Scoring: When paper is folded, it’s sometimes scored to make the fold sharper
Screen-ruling: Halftone dots per linear inch or LPI, I suppose. For example, a halftone screen might be 150 lpi. I’ve rarely heard it referred to as screen ruling, though.
Step-and-repeat: Burning the same artwork onto a plate in a pattern multiple times to create a pattern for a banner or backdrop or whatever. It likely applies to digital too. I’ve heard the same term used in other ways too, though.
Thermal fastening: Like mechanical fastening, there are lots of thermal fasteners, but I have no idea what your instructor is referring to. For example a rubbery sort of glue is used to perfect bind (look it up) the edges of books to hold the pages together, which is different from, say saddle stitching (look it up), which might be referred to as a mechanical fastener, I suppose. Again, though, I’ve never heard either thermal or mechanical fasteners used as precise terms that apply to specific things. They seem awfully general to me.
