Does anyone know if the hAP ac² can do WiFi Access Point and WiFi bridge mode in the same time?
Well the hAP ac² has two wireless cards, 2.4GHz and 5GHz. Are you talking about using one of the cards (2.4GHz for example) to connect to another SSID as an uplink as well as broadcast it's own network on the same card? If so MikroTik supports virtual clients and can achieve that. You can also use the 2.4GHz to bridge and the 5GHz as an access point.
I have done the same experiment as you mentioned. The maximum throughput was reduced by half, i.e., around 120MHz something. The main 5GHz AP was connected to the AP station of the main router. I created a virtual AP (5GHz) and connected to my Macbook Pro Retina.