Create download zip package

1) To download any specific file, you can use the /2/files/download endpoint, and to download any specific folder and its contents as a zip, you can use the /2/files/download_zip endpoint. These will require one API call per file or folder, respectively though. There isn't a way to bundle multiple different files or folders into a single API call. (Depending on your setup/environment you may be able to perform the multiple calls necessary and handle the results automatically in your UI, but I can't provide guidance on that aspect of your app.)

2) To upload a file, you can use the /2/files/upload endpoint (or upload sessions for large files). That's not something that gets "embedded" in your app exactly, but rather just another API call that your app can make. From your description, it doesn't sound like any of the Dropbox pre-built components (the Dropbox Chooser, Saver, or Embedder) do quite what you need but please feel free to elaborate and I'll be happy to pass this on as a feature request if not.