TCP – HTTP Closing Connection with One FIN Package

Yes, parallel HTTP connections requires separate three-way handshakes.

Multiple HTTP requests can be handled in one TCP connection. This can happen sequentially, but since HTTP/1.1, the concept of pipelining allows sending multiple HTTP requests in one TCP connection without waiting for the responses. This results in a seemingly parallel handling of HTTP requests, but note HTTP/1.1 requires the server to send the responses sequentially and in the same order as it received the corresponding requests.

I think you are confused. Did you carefully read what you quoted? The side that terminates can keep receiving data, but it cannot send anything back into the connection.

That means that if the server terminates the connection, but the client does not, the client can send data to the server, but the server cannot send anything to the client. If the server needs to send anything back to the client to fulfill the request, it cannot.

There are reasons for the handshaking, and your desire to speed things up by eliminating the handshaking means that you are using the wrong transport protocol for what you want to do. It sounds like you want to use UDP instead of TCP. Any TCP features you wish to keep will need to be handled by the applications, but UDP eliminates all the handshaking.

Alternatively, you could create your own transport protocol.