In American English, if a person omits the verbs, then there sentences are seen as incomplete, and the listener may think the speaker is uneducated. Also, there are some dialects of American English that such questions would be acceptable, most notably is Black English (aka Street English). But in everyday conversation or in a business/academic situation... the sentences you listed would not b considered acceptable. ~Samantha :)

In informal English we may omit the verbs so all four sentences can be said, particularly 1 and 2. However, 1, 3 4 and "what I want" can be used in correct English too. For example: A: I'm going to the shop. B: I want to tell you something. A: What you want? A: That place I told you about is closing down. B: Where you go? A: I'm trying to figure out something. B: How they know?

informal English is usually far from proper grammar but this doesn't mean a non-native speaker should ignore grammar too because what looks natural for native regarded as ignorance for anyone else