OK, here's a more complete answer, point by point.
1. As I mentioned in the last post, BBAF will activate VR with newer cameras, say anything introduced since the D4. There was a good list in one of the posts that quoted Them Hogan. As someone mentioned, if you release the back button, VR will shut off after a few seconds on its own until you press again.
2. VR does have 2 stages. The first is for the viewfinder, so when you look into the viewfinder the image becomes steadier. The second - and most important - engages when you fully depress the shutter release. At Stage 2 the VR group is re-centered and starts sampling movement again. Only Nikon knows if they consider the data points collected just milliseconds before tripping the shutter, but since the VR group is re-centered when you press the shutter, I'm not so sure they do. As far as I've been able to reverse engineer / research on it, all the heavy lifting for images is done at Stage 2. As for delays introduced by the system when stage 1 and 2 are engaged right after one another with a shutter press, I've never noticed one, but I have no way to really test it either.
3. The big question is if VR helps with AF - and that's a mixed bag. If you've ever used VR, you've no doubt noticed that the image in the viewfinder seems to "jump" when you press the shutter. With the VR group is engaged as you look through the viewfinder the image "floats" a little (easier to notice on a tripod) and, as I mentioned, the VR group re-centers and starts again upon the release of the shutter. You've probably also noticed when this jump occurs the AF point isn't always exactly where you thought it was. My 500PF review has a simulation of this that can help (starts at 14.09
https://backcountrygallery.com/nikon-500-pf-review/ )
I've had more than a few e-mails from people absolutely certain they had an AF point on the eye of their subject, only to have the camera show them it was off by a hair. When I ask them if they were using VR, the answer is always the same - yes.
So, bottom line, is that with VR engaged it can be easier for the camera to focus and for you to control the camera, BUT the AF placement precision is lower. Sport VR can help with this as it adds less stabilization to the viewfinder and you have fewer errors.
IMO, if movement on your end is greater than the amount that VR makes the image jump, then it's a benefit for focus. If not, it can work against you, especially for small targets where you need the best AF placement precision.
4. As for holding a half press to keep VR engaged in an older body, I did it all the time. Heck, I do it with current bodies all the time too. The purpose of BBAF isn't to just focus with a different button, but to bypass the need to go from AF-S to AF-C all the time. See my video here -
https://backcountrygallery.com/free-back-button-af-guide-for-nikon/ Most of the time I have my finger at the half-press point because I'm actively watching and waiting for a special moment in the viewfinder. When it happens, I want to have the meter running (so I can keep an eye on the settings), VR engaged if I need it, and most importantly, I'm much smoother, steadier, and faster with the shutter release when I already have a half-press initiated. In fact, I'm often just a fraction of a millimeter from tripping the shutter in those moments. So, IMO, keeping a half press with BBAF is not a big deal and even a benefit.
Hope that helps :)