Are there any rules for missing words in English questions or affirmative statements?

Question

In some sentences we don't use some words: For example: 1. Instead of: "Do you want a ride?" We say: "Want a ride?" 2. Instead of: "I'm just coming. Hang on!" We say: "Just coming. Hang on!" Is there any rule for how we can make them short?

Answer 1

There is formal English--what we learn in school--and then there's slang which is defined as a type of language that is much less formal and primarily used in speech. What you are referring to are examples from spoken informal English, so there are no universal formal rules. That being said, oftentimes first person and second person pronouns are omitted (I, you), since it's automatically understood when we're with family and friends.