Can't speak for this specific kit but in general: A big problem with lab grown meat and cell tissue culture is that to grow cells in vitro you usually need fetal calf serum. That's a liquid from, well, cow abortions basically, that contains a plethora of different molecules like growth factors and mediators. As far as I know, there is no vegan alternative to this yet. We are talking about a liquid here whose composition is really complex, so it's a really big task to create a plant based FCS alternative that performs just as well.

Tldr: probably the set contains a liquid made from cows.

As vegan as it gets, I'd wager. You need to take an initial sample to cultivate the meat from, which obviously isn't vegan, but to my knowledge, the rest doesn't require any further samples

Likely depends on what's needed/used as feed

Yes it is, as no animal is harmed:
"Veganism is a philosophy and way of living which seeks to exclude—as far as is possible and practicable—all forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose; and by extension, promotes the development and use of animal-free alternatives for the benefit of animals, humans and the environment. In dietary terms it denotes the practice of dispensing with all products derived wholly or partly from animals."

This one is considered vegan because it used expired human blood cells, but calling a cheek culture meat is beyond the pale.

What about this post has anything to do with vеgаnism BudgetBandit