Many native speakers expressing sentences without verbs while speaking,
- What you doing now?
- How you doing?
Is it appropriate?
On the face of it, it is wrong and formally should be "What are you doing?" and "How are you doing?".
These can be shortened to "What're you doing?" and "How're you doing?" and then it becomes a matter of pronunciation and hearing: in some cases the 're can be almost silent and not heard, and so transcribed by the listener apparently without a verb.
There are alternatives: I imagine these may be the origin of "Whatcha" and not that far away from "Howdy", though the latter is more probably from "How do you do?".
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Spoken language differs in many ways from written language. Those utterances would certainly occur in the spoken English of native speakers and to that extent they are ‘appropriate’. Incidentally, each contains a verb, even if it is a non-finite one.