Here is a pretty good example of a file manager app for Android built with Delphi XE5 Firemonkey. It comes with source so should be pretty useful for building something similar. It shows how to create files and folders plus copy and move files and folders. Lastly it demonstrates how to use multiple resolution icons and use a custom dialog box. There are two different blog posts about this demo file manager so I’ll be linking to the second one because the source code is more refined in it. The original blog posts about the file manager demo app are in Russian so I have provided the link through Google Translate for you.
FMXExpress.com has over 700 tips and tricks for building cross platform apps on Android, IOS, OSX, Windows, and Linux with a single codebase and single UI using the FireMonkey framework found in Delphi and C++Builder.
FMXExpress covers top cross platform secrets for FireMonkey in C++Builder and Delphi XE5, XE6, XE7, XE8, Seattle, Berlin, Tokyo, Rio, and Sydney.