The protocol is configurable. Typically you have 8 data bits, 1 stop bit, normal logic, no parity. The baud rate you choose on the Serial.begin() function call.
You could normally connect Tx -> Rx and Rx -> Tx (ie. swap them) and also connect the Ground pins.
The chips aren't really designed to "power up" through the few milliamps that come down the serial pins, however as a general rule you don't pump voltages into a device that is itself powered off. Having said that, it probably won't hurt.
To connect serial ports, I would not be using any resistors at all.
I've documented Arduino serial ports here: