Each TCP connection has 4 values to identify it: IP1 (own IP address), port1 (the port on my end), IP2 (the other computer's address), port2 (the port on the other end).
As soon as any of these is different you are talking about a different connection. keeping this in mind:
computers can have multiple connections active at the time (most of the time they'll choose a different local port from the 65k available),
you can even connect twice to the same server on the same port as long a the locally chosen port is different
same as above, there is enough leeway in the local port range to open multiple connections, (though no-one will ever use 80 as the local port for outgoing connections)
http (like 90% of all internet traffic) is over TCP,
UDP is only used for specialist applications where you are allowed to lose some data