With DS1 I tell him what he CAN do with animals rather than what he can't do. E.g. he can pat them gently. I still have to tell him not to chase them sometimes but it works better when I say "stop chasing the cat, he doesn't like it and you are scaring him. He won't play with you if you scare him" instead of just telling him to stop. Then I usually redirect him to do something else.
I also agree with pp about getting her to feed the cat in the morning. Perhaps measure it out the night before so she doesn't overfeed it but it might make her think of the cat differently.
The running is a bit harder because she is probably doing it when she is excited. If she does it a lot I would tell her every time that she has to go back where she came from and walk slowly. Eventually she will get sick of having to go back and hopefully stop running.
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