I am a batch sparger and I love it.
To address your specific questions. You do not need to stir up the grain prior to vorlauf. Just start drawing liquid out the bottom until it seems to run pretty clear. (And clear means just the large chucks). After that run all the liquid out of the tun. I add more water and stir it up. The stirring is vital at this point to get good exchange of sugar held in the grains into the water as efficiently as possible. There is no reason to let it sit longer, I start to vorlauf right away until clear again.
As for volumes, I mash at my desired ratio. Then I measure how much I collect from the first runnings. I subtract that from what I want my total boil volume to be and add that volume back into the tun. I know there is a rule of thumb out there about trying to equalize the volume of each running, but I haven't found it that important. (And neither does Denny Conn, the dude who has really pushed batch sparging into the mainstream).
For example, if I was planning on getting a 7 gallon wort for my boil, and I draw 3 gallons for my first runnings, I know to add 4 gallons for the second runnings. Its much easier this way than anticipating what the first volume is, adding water prior to run off to get the same volume for your second run.
Here is the link to Denny Conn's Batch Sparging website for reference, but note the changes I mentioned about equalizing the two run offs, isn't his recommended practice anymore.