2004 G35 is running hot with vibrations. Trying to see if it's water pump and if its part of timing chain so if so, will all have to be replaced.

 

Start by verify the fans run and will switch between high and low speed. Turning the AC on should force high speed so you can compare to low speed.
Also pressure test the coolant system.

Plus pull and inspect the spark plugs for the vibration issue.