1) For this, you should check the driver of the device https://wireless.wiki.kernel.org/en/users/Drivers/brcm80211. The Monitor Mode is not supported yet. Have you requested the Product Information for the the BCM43340 in Broadcom?
2) The Broadcom BCM43340 does not have dual-mode Re: Possible to have WiFi AP + Station simultaneously ?
3) I haven’t tested the Arduino WiFi Shield 101 yet. There are some tests for thehttp://https//www.arduino.cc/en/Main/ArduinoWiFiShieldArduino WiFi Shield in the Shield Testing Report [Section 19] and the results were not good by using the default libraries. Take a look at the suggestions in the document.
4) There are no support for Monitor Mode yet
5) Yes, take a look at the Shield Testing Report [Section3] for more information about how to do it
6) There shouldn’t be problems because the shields you are talking about uses SPI and these lines are not connected to the Antenna on the board.