I don't think the knife is a meat-cleaver, the handle is a bit flimsy & the hole at the front & general shape suggest to me it was attached to a pivot point on a board and used for chopping up stuff (like plug tobacco which was an old "worm medicine" and would fit with the veterinary theme of the rest of the gear).
Those other gadgets look like "firing irons" alright. And "firing" isn't a practice of "hundreds of years ago", it was still practiced up until very recently, despite the lack of genuine evidence that it did anything useful, and I wouldn't be surprised if some folks are still at it. One of its supposed benefits was to cause scarring & "strengthen" the tissues around dickey joints. For all sorts of technical reasons (I'll spare you the pathology lesson) it's a silly procedure with almost zero efficacy apart from perhps causing the animal to keep the joint still while nature did its thing & got on with as much healing/repair as it could.
There are quite a few procedures in both veterinary & human medicine that persisted despite their utter lack of real benefit (& in some cases downright harm!) to patients. "Blood-letting" comes to mind - an idiotic procedure that was practised for thousands of years. There
is a condition in which it is helpful - haemochromatosis, a hereditary disorder in which you accumulate more iron in your liver than is good for you. However, that condition wasn't understood until quite recently.
But the wheel has turned full circle and now we have people taking umbrage against genuinely useful therapies like vaccination, which has occasionally done some harm due mainly to human error, but on the whole has had immense benefits for both mankind & animal-kind!
Strange creatures, human beings....