I would like to build an external asp.net mvc application that has the following features:
My questions are as follows:
you can use Google Drive as the storage solution for your application, check the Google Drive SDK: https://developers.google.com/drive/
Google Drive application usually rely on the users' accounts to store their files, but nothing prevents you from using your account to store all files and make them publicly accessible
there's an ASP.NET MVC tutorial and sample app at https://developers.google.com/drive/examples/dotnet, however, it authenticates each user with his own account. You can start from it and replace the standard OAuth flow with one that always uses your credentials, for instance, by always using a Refresh token that you generated in advance and provided to the app.