What you are describing is the exact purpose of Kentico's Web farm feature where you can have multiple servers (web farms) connected to a single database. The main purpose of web farms is to ensure that cache and files (not code files, but media files such as the ones uploaded by you as attachments, media library, meta files...) are synchronized across all servers.
Each server in your scenario has its own memory and if you change an object, you want all other servers to reflect the change because otherwise some visitors might end up seeing "old" data, while others wouldn't.
You are also correct in assumption that all code files (ascx, cs, aspx...) will need to be uploaded to all servers. Best way to approach this is to have a tool such as Team city which is able to deploy your changes to multiple servers simultaneously.
With js, css, html, images... it depends where you store them. If you store them in database (not usually the best thing to do) you don't need to update them on particular servers, but if you store them on file system, you might need to. There are many variables here, but some deployment tool will probably be the best bet.
