Am I able to have Alexa interactions via my mobile phone while on the Mobile App Private mode?

Yes, you will be able to have normal Alexa interactions via your mobile phone while on the Mobile App Private mode as long as your BuddyTalk Mobile App is connected to the the BT110 device.  Note that the BuddyTalk Mobile App can connect to the BT110 device when they are both connected to the same local network.

On the other hand, when you are using an analog phone connected to the BuddyTalk device RJ11 port, you cannot have Alexa interactions through the RJ11 analog phone set.  However, while you are on the RJ11 analog phone set, the BT110 device’s microphones can still pick up your Alexa command if your voice is within the BT110 device’s pickup range, and the Alexa response will play out through the BuddyTalk device speaker.