Not sure if you should be dry hopping a Berliner Weissbier (same thing as Berliner Weisse). The style should have little to no hop aroma, but it’s your beer so if you want to do it, dry hop for no more than three days. If you can cold crash the beer ahead of time, all the better.
Adding fruit puree at the end of fermentation will most likely restart the fermentation because of the sugar in the fruit. As long as it is aseptic, as you say, it wont ruin the beer. i might either add it toward the end of fermentation before you hit terminal gravity or at the end of the boil before transferring to the fermenter which will make sure the puree is sterilized. Others may chime in on this and offer better suggestions.
Good point about the style. Yes, I don’t want it to taste dry hopped to the extent that you’d put in on the label, but just as an experiment. It would be no more than 1 oz of Crystal.
Right now the plan is to, as you said, add the fruit toward the end of fermentation.