Is there any truth to the fact that vorlauf should take X amount of time?
Is there any timing requirements to the speed of adding water back into the mash while sparging?
Actually, what you are doing when draining the tun is called "lautering." That's why the combined use device in which you mash is called a mash/lauter tun. Most brewers used to refer to the step as lautering until there was a need to distinguish the technique that a brewer was using to separate the sweet wort from the grain (yes, there was a time when most all-grain home brewers continuous sparged).
There is really only one type of sparging because the word "sparge" is derived from the Latin word for sprinkle (i.e., sparging does not technically occur until water is emitted from the sparge arm). The batch sparging process is more accurately defined as multiple-infusion lautering because the first runnings are lautered followed by one or more hot water infusion/lautering steps. It's a modern twist on a old technique known as "parti-gyle brewing;" however, with parti-gyle brewing each runoff was usually used to make a different beer, not combined into an "entire gyle," as occurs in batch sparging.