¿Dónde se almacenan los archivos descargados en Android?

They are stored in device's internal storage, if you haven't chosen to store it in the sd-card. Internal storage make use of linux file system permissions, so files will private to your application and other applications cannot access them.

If you are talking about media files, you can make them accessible everywhere by adding them in their respective content providers.

Para abrir un archivo use openFileOutput() which return a file stream.

You should read the article on Opciones de almacenamiento which also provides a code example for accessing the external storage.