Corrections in red. Stylistics in blue.
What happened to Anton?
1) Anton! What a terrible bite! What's the matter? You beat? [1]
2) It's okay, don't worry
3) Oh, poor thing! What happened?
4) Well.. Remember I said that I wanted to have a pet?
5) Of course I remember!
6) Well, I was given a little puppy. I called him Andrey. And it turned out, he loves to bite! But I still love my new friend.
7) Oh, that's so cute.
8) Now I will take Andrey for a walk in the park. [2] Will you come with us? Variants: Do you want to come with us. Would you like to come with us?
9) Of course, I'll go. Only, let's buy him a muzzle.
10) OK.
[1] I don't understand what you mean by "You beat?" Please paraphrase in English, or write the setntence in Russian, and I'll try again to help.
[2] When more than one person does something with another person, Russian speakers often say, "Мы с (кем-то) ...." In English, we do NOT use that construction. Так, нельзя переводить дословно с русского на английский, то есть нельзя сказать, "We with him are going to the park." Instead, we say, "(Someone) and I....." Example: "Мы с ним пойдём в парк." = "He and I will go to the park." The same construction can be used even though "Andrey" is a puppy, not a person. However, it's customary "to take" a dog "for a walk."