In conversation or informal writing, do native English speakers often drop an object when it is understandable which object is dropped in a situation or according to context as in "Give (the book) to me", and "submit (the report) to me"?
No. W say "Give it to me", and "submit it to me". Clive
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fire1do native English speakers often drop an object when it is understandable which object is dropped
Not often, and not in examples like those you asked about, but once in a great while the object is dropped when the object is very clear from the conversational context.
— Are you still playing tennis these days?
— Yes. In fact, we