Karen feels like she wants to live with an animal. She always likes to be surrounded by animals. One day, on her way home, she passes by a cat shelter and decides to adopt an old orange cat. Since that day, Karen is very happy, they (who is "they"?) have started a family, and she is thinking about adopting another cat. You made no grammatical errors. "Karen has been happy" would be more correct than "Karen is happy", but I like the sound of "is happy" and it's not wrong. Likewise, it would be more correct to say "she passed" and "decided". However, once again, I like the sound of the present tense because you are telling a story, and the present tense makes the listener imagine that it is happening right now.