Can we use the opened websocket to send data to the server?

I understand the current purpose of the live query, where we subscribe to a query and the client receives events if there is any action that matches that query. Is there any way that we can use the existing socket connect that we’ve opened to send the data to the server for some other purpose?

I’d say no. There is no such feature. You could try to use the connection in place by inspecting the objects and send the data but I’m afraid that live query could stop working because there is a specific protocol for the messages. Probably it will be easier to just open another web socket for other kind of messages.