No, you cannot omit "do". This is the standard question form. Students learn this at elementary level. If you ask "Which one you prefer?" or "What you mean?", I'll understand what you mean to say, but you'll definitely sound like someone at beginner level in English.

No, you must use it because "do" is the auxiliary of the senteces and it works to make the interrogative forms

I think that you actually want to ask "Can you get rid of the word "do" in these examples?" or "Can you remove the word "do" in these examples. "Miss out" generally refers to an person's experience. For example "You missed out on great practice since you skipped class."