Today my student Valentina invited me out to dinner. Being an animal lover, she dreams of becoming a zookeeper one day. This gave me an excuse to take my bunny Sweetie along, and he got along pretty well with her. While away from home, Sweetie seemed alert, unafraid, and friendly with strangers. If I take him out for walks more often, I believe he will get used to the world outside and start exploring. We had a really good time. Sweetie attracted the attention of some passersby. Some friendly shop assistants tried to introduce him to a kitten in their shop. But, having never seen such a creature before, the kitten was scared.
"passersby" does not have a hyphen.
Your grammar is excellent. You need to work on style.
You use too many compound sentences, but this is only a symptom of a deeper underlying problem: you are not connecting your thoughts together.
Look at your second sentence for example. It is really three complete sentences that have no compelling reason for being together in one long sentence. Your third sentence is two sentences that have no reason for being united into one. Your fifth sentence ("We had a really good time...") is also two sentences that have no reason for being together. Your last sentence is three complete sentences in one that are not tied together in any meaningful way.
You can do a better job by deciding first on your main thoughts. Each sentence needs only one main thought, one main subject, and one main verb. The related thoughts that are less important can be changed into subordinate phrases or clauses. When you do join two complete sentences into one, make sure you have a good reason for doing so.