"Es José" is grammatically wrong. It seems like a word-by-word translation from English. I don't know if it is used somewhere, but here in Spain it sounds completely wrong.
"Me llamo José" could be used when calling an unknown person. Like if you are a sales rep or something, and you want to introduce yourself: "me llamo José y le llamo de la compañía X..."
Learning a language, like with learning most of other things it is not only about knowing what words mean and being able to express your thoughts. It has to come automatically and without having to think about what every word might mean.
I have learned two languages and am learning a third one. The problem you describe has been common to all the languages ...
This depends a lot on the culture, so, as they say, your mileage may vary. For me, using honorifics is mostly out of the question except for señor or señora. Using señorita for unmarried women is still heard of, and there's no suitable neutral replacement equivalent to English Ms. Female kindergarten and primary school teachers are customarily termed ...
If it's been a chatty, longish interaction, you need to indicate that you're ready to wrap things up, as preparation for saying good-bye. Here are some ways to do that:
Bueno, pues, (name of person), fue un placer. Luego hablamos, ¿eh? (response) Saludos a todos.
In Venezuela, I learned to always respond with the form "Habla José," even with friends and family. I think that the formality of the statement will vary from country to country, but grammatically, at least, it's correct and fluent Spanish.