When I take off the gas cap, there is noise from the tank like pressure is released every time. Is this supposed to happen? Would this also affect the gas gauge reading full all the time?
The gas gauge measures the level in the tank by a float lever, not by pressure. So this doesn't affect your gas gauge.
The overpressure in your tank is completely normal. Gas has a relatively high vapor pressure, which means it tends to vaporize easily and even builds up a pressure when enclosed in a tank.
Modern cars have to avoid the emission of fuel vapor into the environment. They allow some overpressure in the tank which also reduces the rate of evaporation. If the pressure is too high, it is released through a active carbon filter.
The first part of your question has already been asked here - Why is there a hissing noise when I open my petrol cap?
It is normal for a fuel tank to do this.
This will not cause your fuel gauge to show full all the time. Your fuel level sensor is probably faulty.