If I understand right, applications sometimes use HTTP to send messages, since using other ports is liable to cause firewall problems. But how does that work without conflic
You need to be careful in making the distinction between "listening on port 80" and "connecting to port 80".
When you say "applications sometimes use HTTP to send messages, since using other ports is liable to cause firewall problems", you actually mean "applications sometimes send messages to port 80".
The server is listening on port 80, and can accept multiple connections on that port.