Is there a name or standard for the format a curve is converted into the string that we copy/paste a curve using the Apex manager app? (I’m assuming this part isn’t proprietary)?
It's base 64 encoding, I think the standard was originally for email like MIME encoding or something. I wrote the encoding parts for this quite a long time ago though. Feel free to take a look at the source, but be warned it may be spaghetti code as I figured out how the encoding worked.
To view the source, just open the HTML in your favorite text editor.