It is possible to achieve two-way communication between a client and server using Server Sent Events (SSE) if the clients send messages using HTTP POST and receive messages asynchronously using SSE.
It has been mentioned here that SSE with AJAX would have higher round-trip latency and higher client->server bandwidth since an HTTP request includes headers and that websockets are better in this case, however isn't it advantageous for SSE that they can be used for consistent data compression, since websockets' permessage-deflate supports selective compression, meaning some messages might be compressed while others aren't compressed
Yes, it's possible.
You can have more than 1 parallel HTTP connection open, so there's nothing stopping you.