No they are not protocols, they are functional devices, available as integrated peripherals or discrete devices.
UART and USART are basiclly the same, they do the same job of converting serial data but the 'S' (synchronous) means it can also package and extract bits at a speed decided by an external cloock as well as an internal one. It's a confusing difference as most UARTS can also be used synchronously.
Connecting RX to RX will not cause any harm as they are both inputs and there is no source of power to damage them.
It is possible to cause damage by connecting TX to TX because one could be driving high while the other drives low and hence short out the power souce. However, this is unlikely to happen because most serial drivers these days have protection of some sort and those generating their own RS232/V24 voltages usually can't provide enough current to damage their output stages.
A protocol is the method used to prepare the data so it can be sent serially and recovered reliably at the other end of the link. Sometimes this is done in hardware, sometimes in software but it has nothing to do with the electrical signals present in the link.
Brian.