The cam should not use external bandwidth to any significant degree when you are viewing point-to-point inside your network. Exceptions are some periodic maintenance handshakes to keep connections available in case of an authorized external request, like you outside your network, or a share you made with someone.
You are streaming any time you are viewing the image from the camera. So viewing in Bluestacks is viewing the live stream.
I don’t know the efficiency of Bluestacks, but if the sluggishness is on the same device, it may be because of CPU loading. If it is on another device, then it could be because of router loading, if your router is a low-level model.
Yes, the cam will become warmer when it is transmitting.