Is there a way to upload to app_data from the admin dashboardSure - on the System perspective you have a folder marked "/" which is the website root - this expose your entire website structure. Open it, right click App_Data and Choose upload.
Is there a way to see the file structure from somewhere without going through the files? (for example, if I wanted to link to a media file manually).All code editors (css, less, xhtml, templates) have this - click "Insert" button and select "Front-end URL". This will expose the same file structure as you can see on the Layout perspective (folder structure starting with "/"). This is a 'filtered' view on all files in the website folder.
If you want more folders to be exposed here, go the the System perspective, browse to the folder (starting from "/") and when you find the folder, right click it and select "Show in Layout". Then the extra folder is included next time you browse "/" in layout or you use the "Insert | Frontend URL" feature.