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I'm also rather new to LiveKit, but I've seen their spatial audio example, that may help you with the music streaming bit https://github.com/livekit-examples/spatial-audio

For the queuing system, you can use participant metadata to handle this. When a participant enters the queue, you could include a field with the current timestamp. That should allow you to sort the queue on the client side. On synchronization, yes, it'd be better to ensure that music and user's singing come from the same machine. That is the best way to ensure there are no unexpected latency between different sources.

Thank you very much for your responses and the time you have given.