1- Can you please tell me the TX and RX pins on Arduino is connected to which pin on on LCD?
LCD pins are:
Vss,
VDD,
Vo,
RS,
R/W
E,
DB0-DB7
Serial LCDs don't have those pins. That yours does means that it isn't a Serial LCD. So, none of the pins are TX/RX.
2- I want to type in characters in Aurdino software and be able to display it on LCD in real time using USB cable.
You have a keyboard attached to the Arduino? Is your LCD attached to a USB cable? Is it a USB host or a USB client?
3- I am using the below code, am I using correct code ?
Not even close.