In the past I worked on many UI based apps, for mobile, applications like "Guess the Flag" etc.. Your app idea is relatively easy to make, we will make sure that everything looks the same on different screen sizes, different resolutions, different mobiles (iOS / Android).
For the stamps, we will create a variable, and depending on the value of that variable, the application will decide what icon needs to be stamped. For the drag and drop it's pretty basic coding, as well as the zoom or rotate.
I am looking forward for your response.
Best Regards,
Vlad T.