I've been studying Arduino Nano schematic and see that there are 1k-Ohm resistors on the TX and RX lines between ATmega MCU and FT232RL. Are these resistors necessary? Or would it be possible to have these pins connected directly without resistors? And could someone enlighten me on the reason behind these series resistors?
They are both optional and necessary
Optional because no, they are not truly required. Necessary because people tend to want to communicate with other devices over serial. So you have the situation where two devices are both trying to drive the same signal, and that can burn out the devices if one drives high and the other drives low. With a resistor in series, the current is limited if one tries to drive high and the other tries to drive low, so the devices are protected.
The Gadget Shield
: accelerometer, RGB LED, IR transmit/receive, speaker, microphone, light sensor, potentiometer, pushbuttons