Morals of animal consumption aside, adding demand for any part of an animal will add some degree of financial benefit for using animals in general (ie: reducing waste by making use of an additional part means more $ in the farmer's pocket per cow).
Well, maybe. By finding a valuable use for an otherwise unused part of the animal, you're increasing the value of raising and slaughtering animals, and increasing the value of something usually encourages more of it. But it's more interesting than that because the main market is for the meat, and if the availability of meat were to decrease because it's not as profitable, one would expect the price to go back up a bit, which would in turn encourage more production.
That's a strange way to frame it. Reducing waste will allow farmers to cover more of the production costs using non-meat revenue. In a competitive market, this will push them to lower the price of meat, stimulating its consumption, and increasing the number of animals, which in turn will lead to economies of scale, lower costs and prices, even higher demand and even more animals.
You don't know the elasticity of demand for the non-meat parts. Parent was hypothesising that the demand for it might be inelastic so the price would go up.
Further, a lower price for meat may stimulate demand but it will more likely suppress production rather than increase it. It depends on the costs of raising the animals and the opportunity costs of the farmers. Excess profit is what generally attracts competition and more production. Lower prices are not normally associated with larger profits. Only a few "markets" are much different; e.g. oil, gas, etc.
There's two sides to every price setting action, supply and demand. The current price is where they cross now, so the shapes of the respective curves aren't necessarily clear.
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Further, a lower price for meat may stimulate demand but it will more likely suppress production rather than increase it.
You might have missed the premise where the reduced prices in meat are a direct result of competition and increased profits due to better margins on non-meat products. The specific demand elasticity is irrelevant for this scenario - as long as pig hides and lard are not Veblen goods.
If more consumer money is put into the animal product market then there are two possible outcomes: either they all go into the profits of the manufacturers in a perfectly monopolistic market, or they go towards higher quantities being produced in a competitive market. It's economically impossible to depress production by increasing demand for the products of a certain industry - except very particular market anomalies, luxury and status goods etc.
Very unlikely as it's basically a way to get value out of low value parts. If sources on Wikipedia are to be trusted it's mostly made from pig and cow hides, which is why you can also find kosher gelatin (where the supply chain is known and free of pork products).
Probably not. Lot of parts can produce gelatin and they are usually not the ones eaten or are less preferable. So actually I think it likely did reduce waste.
