For the first part, no. Without "do", the question now follows a statement structure and sounds like it should be part of a sentence: "...and that is why these things all happen to me"; "The reason why we keep doing that is because..." If you tried to ask it as a question, you'll sound illiterate. For the second part, also no. You're using a modal verb (will), which doesn't stand alone. "Be" is the verb in the sentence, and "will" only modifies "be" to give a future tense (in this case, a promise). Without "be" in your example, you simply don't have a sentence.

Yeah, like the most notorious one, "How you doing?"

situation 2 always needs the "be" because it's not in a question. As for "be" or "do" in questions, in spoken English, when said quick and lazily enough, you can leave them out. Why (are) we doing this? What (did) he say? Where (are) you going? Etc. Do tell it from the situation in clause, though. "I know what you did."

All of your questions need the do or be in them.