Re: at the picture ... and if you say 'at the picture' you run the risk of being misunderstood, with people assuming you mean 'at the cinema' [at the pictures].
I don't think I've ever heard 'on the picture' either, except in reference to either a physical arrangement or to something added after the photo was taken: 'the coffee-cup is on the picture'/ 'there is an ink splash on the picture'.
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