I believe this exclusively uses WiFi direct and skips the AP completely, but I can't completely confirm with a quick google.
Yep, it does - the underlying technology is based on Miracast and works only with Wifi adapters made by Intel because it's point-to-point. Sadly it doesn't work through an AP connection at all.
Works simultaneously here, Intel and most phones support multi-role.
Yes, I just mean it doesn't work over your WiFi connection, so you can't connect another device elsewhere on the network, it has to be in range.