Hi.There exist some ways to do what you need. For example you can use triggers and shortcuts. A trigger for --->picture in picture (talking head and video side by side) this input like "on transition in"-->output-->set output fullscreen-->output or the real input you need or a mix input and it will send your main pgm into the room.Then reverse it-->"on transition out"-->set output fullscreen-->a black input or mix input if you need to change easy between 2 states in the fullscreen out.
For audio. Inside the room you have speakers,tv monitor audio from hdmi out?
A way is to go to vmix-->settings-->audio outputs and in the bus A to G you have to select the output device that is connected to the room. For example BUS A. Then in vmix audio mixer,for any video/audio you need to be listened in the room,you will press on it the "BUS A" button
You dont press it for your mics,because then the talents will hear themselves and have echo. Also for audio on/off inside the room,you can combine the "on transition in"/"on transition out" with audio bus on/off to be able in the room to hear or not the audio of any you need.
There exist in yt a lot of videos explaining scenarios like you need and you can do many combinations