It's great to have you here @Uruzu5! Currently, it's not possible that Fitbit Ionic connects to corporate Wifi, it will just connect to open WEP, WPA personal, and WPA2 personal Wi-Fi networks. You can learn more about it by checking How do I connect my Fitbit watch to Wi-Fi?.
In regards to your second question, I'm not sure if I understand at all. Would you like to just stop playing the music in your earphone and then next time it should connect automatically? If you don't unpair your Bluetooth earphone from your Ionic, it should connect to it next time. You can learn more about it by checking this article How do I connect Bluetooth audio devices to my Fitbit watch?.
Keep me posted!
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