Do I have to install a particular ADMIN PosgreSQL tool in my Cloudron application to see & administer this Mastadon database?
You can use the Weberminal to get shell like access.
On the top there will be button for Database access.
And to see all my files & their paths in a UI do I need to install a separate directory or file browser in my Cloudron application?
Like the Web Terminal you can use the File Manager to see your files.
The path in the File Manager is always /app/data/.