This is cool. Some time ago Peter Foot created a MediaElement control for Xamarin Forms for displaying video (and audio) content across the main mobile platforms. He has started the process of integrating the control into Xamarin Forms itself with a Pull request opened last week. This should be a great enhancement for the framework.
Xamarin Forms MediaElement by Peter Freeman Foot
When it comes to file handling and Xamarin Forms you can find all you need in the official Documentation. But there are some platform specific considerations.
Storing files is not tricky but put some thought into where to store your applications data can go a long way. Xamarin.Essentials may provide all the functionality you need, but if not you usually use the System.Environment.SpecialFolders and the System.Environment.GetFolderPath to get access to different folders offered by the platform you are on.
Xamarin Forms and the open Question of where to store your files by Mark