>>15326
All very good questions! I have never been much of a worldbuilder so I will have to take my time with these. But I would like to answer each question in separate posts to extend the life and content of the thread.
>cow's place in society
I feel this one may have some overlapping answers with your 4th question about the institutions they would run. But if I had to guess, I think many would lean towards manual labor jobs, usually involving agriculture, but plenty of holstaurs would work jobs a little different from that or outside of that entirely.
It would be no secret to any cow that milk is a special resource only they can provide in mass quantities and they would play to that strength by using it as ingredients in food. Cow baristas and bakers would be plentiful in more urban areas. There would probably be at least one in each bakery, coffee shop, possibly even bars, breakfast restaurants, and any place that serves food or drinks that use or complement milk well. This would further give them a firm place in society as food providers which would also support the easy-going, friendly, and nurturing perspective society looks upon them with. On top of that, careers involving children may come easy to them such as nannies or teachers for their personalities and common household skills which leads into the next topic.
On another side of this question: cows are very social animals and I think some animated movies have portrayed them as such, with gossip being common for them. I can easily see them working jobs that prioritize information such as news presenters, reporters, journalists, and possibly even law enforcement. Even within those aforementioned blue collar and entry-level jobs cows would likely be some of the most social in their workplaces. Noticing, collecting, and spreading information would likely be a deep part of their culture. I can see this trait allowing them an easy integration process into society and likely their greatest strength.
As such, the tanukis and foxes might not be terribly fond of them, as their plans would be found out quickly, in some cases due to high intelligence in cows and in others simply because they noticed something was slightly off and were able to collaborate with other cows with the speed at which word travels. Baphs would hate them for the aforementioned reason and with the added reason of breast envy with their attempts at seduction sometimes foiled by cows should a baph fail to ensnare a man quickly.
My memory of MGE is foggy but I think cows would get along with most species due to their friendly and social nature. I would imagine most women of any kind and species would enjoy at least a little bit of gossip, especially in a world filled with women hunting for a mate. They might get along especially well with harpies and gargoyles for being the eyes in the sky that can observe all kinds of events at any place or time. I think they would also get along well with Ratatoskrs, Cu-Siths, Ant-Arachnes, Cait Siths, Nekomatas, Werecats, Kobolds, and quite simply any other species that is likely to hold a close proximity to humans for how much information they would be able to trade with them.
The more I think about it, the more I feel that cows could actually be jacks-of-all-trades in society. Anything they lack could be compensated by simply making friends with others who could teach them skills and knowledge they need for anything they might want or by simply networking their way into jobs they want. The only thing holding them back would likely be simple interest as they may be too easy-going to reach for the heights they could achieve. As such, in agriculture, food, and information they will usually remain and that's just how they like it.
There is probably more that I should say but that is the most my tired brain can think of right now and I must tend to other things. I will spend time thinking about their preferred prey, which I think would have changed over time loosen their preferences as they evolved away from minotaurs. I say all this with holstaurs in mind since they are my favorite species and I often forget about minotaurs but those may have to be a separate post for the sake of organization.
I hope more people will come to love cows!!