The file manager is just a crude tool for downloading and uploading files. Its much easier to use an FTP Client like FileZilla so you can download and upload whole folders at a time easy with drag and drop.
No matter which tool you use, the process is download, edit, then upload.
Sounds like you are just clicking a file in file manager and maybe it opens in something usefull like Notepad, but then when you save it, its being saved on your local drive somewhere not on the server. You can't edit files directly on the server. Best to download the files to a local folder, make your edits then upload.
So ideally, you connect with FileZilla, download the turnitup folder, rename it to happasmama1 then upload the whole folder and then got to site settigns and change your skin to hapapasmama1.
Now you can download the individual css files as needed, edit them locally on your machine and then upload it back to the server.
Be careful making edits to layout.master, if you do something wrong there it can break your site, be sure and make backups of any files before you change them.
Hope it helps,