I am a little confused by your questions as well and although I think Twinspoppa explained it quite well (and I agree with him) let me try to explain it a little further in a bit more detail...
1. BMW does not recommend rotating tires. Just an FYI, and one with which I completely agree.
2. For staggered 19" or 20" tires, you can forget swapping tires on the same side front to back. This should be obvious.
3. Because the inner side of each Vredestein tire must have the longitudinal groove, meaning each tire has a dedicated inner side and dedicated outer side (in other words the tires are
asymmetric) (see drawing A; LI = Left Inside, LO = Left Outside, RI = Right Inside, RO = Right Outside) you cannot dismount a left front tire from it's rim and install it on the front right rim with its outer side now on the inside and its inner side now on the outside. (see drawing B). If the tires were symmetric then you could do this, but they are not.
4. Again, because the inner side of each tire must have the longitudinal groove, swapping tires left to right and right to left
would result in the proper orientation relative to outer and inner edges,
however the direction of rotation would be the opposite. Tires that were traveling in the forward direction are now traveling in the backward direction. (see drawing C)
This is considered okay by Vredestein since the tires are
non-directional.
However, you need to understand a few things. Rotating tires in this manner will NOT extend their life from wear due to camber, toe-in, toe-out, issues, etc. Again, because they are asymmetric tires, inner edge wear will always be inner edge wear just like outer edge wear will always be outer edge wear. However, wear caused by braking and acceleration forces can be compensated for by this type of rotation and can extend the life of the tires. Officially Vredestein recommends if you are going to rotate them, to do so every 7,500 - 10,000 miles.
(FYI: If you watch the youtube video that is linked in the first post of this thread, at 6:24 into the film the narrator specifically states the tires are asymmetrical but non-directional)
Now, for many the question comes down to economics and time. Is the extra mileage that you might get out of rotating the tires as caused by acceleration and braking more than the cost to take the car to the tire shop and pay to have each tire rotated and rebalanced? If your tire shop does it for free then maybe so if you have the time. If not free then I'd say the decision to do it is a little harder to make. It also depends on how you drive, quite obviously. If you accelerate and brake like a maniac, the wear due to those forces will be a lot different as compared to the person driving their kids to school and back at a leisurely pace. Ultimately the decision is yours to make.
My personal suggestion is to:
#1. Buy the tires. It's the deal of the century, especially on a set of 20"'s.
#2. Go to a dealer or indy and have your suspension looked over to make sure nothing needs to be repaired or replaced. If you discover this later, you'll likely need to get the alignment done again.
#3. Locate a tire installation shop that uses the same Hunter tire
mounting equipment that BMW uses, I believe the Hunter TC3500 or better. If you have super expensive rims and don't want them scratched up then I suggest you seek out a place that also has the Hunter Auto34 system which is specially designed not to scratch or mar rims.
However, more importantly, find a shop that uses the same Hunter tire
balancing equipment that BMW uses (GSP97BMW Road Force Measurement System with StraightTrak LFM, which is the OEM version of the GSP9700 Wheel Vibration Control System).
GSP97BMW Road Force Measurement® System
You can locate a shop with this tool:
Hunter GSP9700 Wheel Vibration Control System
Call them up and make sure they have the equipment, just to be safe. Schedule an installation and get it done. Also start making arrangements for alignment. As a rule, full alignment should be done whenever you are installing a full set of brand new tires.
#4. Immediately go to your BMW dealer and have a 4 wheel alignment done. You can of course have this done at a tire shop. If so, I would suggest again that you make sure they use the same Hunter equipment BMW uses (I believe it's the Hunter KDS II Wheel Alignment System) and that you are comfortable with their policies should the alignment not turn out okay. Personally I've had too many bad experiences with tire shop alignment to waste time with anyone other than the BMW dealer for this work. To me the extra money the dealer charges over a tire shop is well worth it.
#5. IMHO don't bother with rotation, per BMW's advice, and just replace the tires when sufficiently worn.