I may be being ignorant here, but I have been researching for the past 30 minutes and have not found how to do this. I was uploading a bunch of files to my server, and then, prior to them all finishing, I edited one of those files. How can I update the file on the server to the file on my local computer? 
Bonus points if you tell me how I can link the file on my local computer to auto update on the server when I connect (if possible of course)
I don't know your local computer OS, but if it is Linux or OSX, you can consider LFTP. This is an FTP client which supports SFTP://. This client has the "mirror" functionality. With a single command you can mirror your local files against a server. 
Note: what you need is a reverse mirror. in LFTP this is mirror -r
update file on ssh and link to local computer