Colloquially, people tend to speak in "shorter sentences" and leave out words like pronouns and verbs such as do, be and have, especially when it's clear who or what they're talking about. They might also omit whole phrases:
Do you want me to try getting the shelf off for you? -------> Want me to try?
Another example:
Are you sure you've got time? -------> Sure you got time?
Now, what are the shortened versions of the following sentences?
Would you like a drink?
Do you have any green tea?
Are they shortened in the same way as the examples below?
Do you want a drink? -------> Want a drink?
Have you got any green tea? -------> Got any green tea?