Will BigIP automaticly close TCP session after a HTTP request

Actually, the longer answer is that it depends. If the client request is HTTP/1.0 and includes a Connection: Keep-Alive header, then BIG-IP will not close the connection. Similarly, if the client request is HTTP/1.1 and does not include a Connection: close header, then BIG-IP will not close the connection. However, if the server returns a Connection: close response header, then BIG-IP will propagate the close unless OneConnect transformations are configured. There are some subtle issues with certain status codes and early shutdowns, but that's the basic idea.