I would like to know whether
\today gets time off of a time server or the system clock, and when. Does it get the time when compiling? Upon viewing the document created?
Surely, it gets the system clock, since if it wants to get time of a time server, you have to be online all the time; but as you know, you can easily compile your code, even if you are offline and not connected to internet.
Question #2: when you compile a document, the output will be created and you can see that, whenever you want. While seeing an output pdf, no change will be happened for that pdf file.