Have you seen my dress anywhere is what English people actually say, come on.
When looking for the dress we use "anywhere" in Australian English and probably English English too.
"Have you seen my dress somewhere?" could imply that you saw the identical dress in a shop somewhere else, so creates unnecessary ambiguity.
The English tense is wrong! Have you seen my dress somewhere, is present perfect and correct here (looking to put dress on or in wash). Did you see, is a simple past question
I agree. In the context of this sentence both 'somewhere' and 'anywhere' means exactly the same thing.
I also have to speak up for the use of "anywhere". It's standard use in the USA too.