It appears as though the device starts up in DTM, although the Manufacturing Bluetooth Test Tool issues vendor-specific HCI commands as well, such as the continuous transmit test.
CTS is used for flow control.
I wonder if it can simply be tied low, as Bluetooth test boxes do not use CTS. 2-wire interface only.
You are correct.
1) CYW20706 has HCI UART over which you can send HCI commands directly (be it for testing or other purposes).
2) You can use the MBT (Manufacturing Bluetooth Test) tool to send HCI commands to the device.
3) Yes, you can pull CTS low and use the 2-wire interface to send HCI commands.