Can you use images from Google in the logo?
No, an image from search is not yours and it cannot be cut into the sign or the cup. Yes, you can look at the neighbourhood to see what you do not want to resemble, and the drawing is made new.
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If a downloaded icon is already in use, say so before anything is printed. The same icon shows up on another bar and on a shirt that is not yours. The mark drawn from scratch, with nothing taken from search.