1)End of August through September and in warmer zones I have read you can go into October. The growth you cut off (scion) is showing for next years buds. These here are present in early August, at least. Each resource I have seen gives the same time table, without further explanation. It may be to schedule it during the normal "fall peony planting time" table that creates the window, allowing roots time to establish before cold ground sets in.
2)This part may be a specific I do not know or understand fully. This may be the reason for the 30%-50% success rate though.
3)I planted in moist soil and did not water in after planting. I was worried about the saturation of the grafts. The plastic I used was opaque and blue. I would choose white of those you listed. The main purpose is to protect from excess moisture. So I would think any thick plastic would do.
Thank you for your comments, Rick.