It would depend on the outfit, but she would be unlikely to agree to anything without getting something in return. She also currently doesn't know Carmine very well, so it'd be a lot of work to convince her, but still not impossible. As for after Cutepocalypse, well, the chances of her agreeing would be close to zero. Before and after Cutepocalypse, Lyssa would say no every time. Vivian would ask to at least see the outfits first, and if she found them to be cute as well (which she probably would), she would totally agree to it. Vivian loves cute stuff.
While Isabelle definitely loves food yeah, she'd be rather offended if that became her ringtone against her will. While she wouldn't know for sure, chances are that the cat being referred to is supposed to be her, and she does not like being called a cat.
Upon finding the cat named after her, Isabelle would not be very amused and would assume that someone was trying to play a joke on her, because the visual similarities are definitely not a coincidence. Lyssa might laugh a little before realizing that something like that might be considered offensive. She would assume that it was someone making fun of Isabelle, and while it is a creative joke, it's not very cool to do that. Vivian wouldn't make the connection, seeing as she doesn't know Isabelle very well. If nobody was around to claim ownership of the cat, she would pick it up and make an adventure out of trying to find the owner. She would make sure to be very careful though, because metal arms.