During eclipses I am unable to guess the model numbers of your equipment so I can only give you general answers.
1. If your stereo system has a BT receiver so you can send audio to it that won't help you, You would need to connect a BT transmitter to the stereo. Connect it to a headphone out or record out or use a speaker to line level converter with a speaker selector.
2. If your stereo system has an audio input and the TV an audio output and they aren't the same type you will need a converter.