I will use a 10-K-ohm pull up between the C8051F120(3.6 V) and JHD162A(5 V), to make the pins swing till +5V, i will have to define the pins as Open-Drain.
just remember that it will (probably) need some 'pulse stretching' the risetime will not be great

1. How would a pin tied to GND or High Impedence affect it's output state when it is open - drain ?
do not tie a pin to gnd

2. Should a pull up resistor be between, Vcc and input, because if the pin is tied to the GND, how would it work ?
why do you tie pins to gnd?

3. Will i have to connect all the 11 lines ( DB0 - DB7 & EN, R/W, RS) to the pull up resistor ?
all pins that are input to the LCD

4. Does the LCD ever give out any signals back to the MCU, or it justs takes all inputs ?
most (I do not know yours) LCDs have a 'ready' signal, you can skip it using wait loops