I don't understand the concept of grounding a circuit for safety reasons, in this circuit that I simulated, imagine my hand touching the circuit as the closed switch. I am creating a closed loop between my body and the circuit letting current to pass through me. If the circuit was isolated or floating however, it would be impossible for me to get zapped because there would be no closed path for the current to flow in and out. So what is the point of connecting the circuit to the earth ground? And secondly, does connecting any point in a circuit to the earth ground pull the voltage in that point to the ground level?
Ground used for safety is a completely separate concept from the ground in low-voltage circuits. While the latter is just a reference point with low impedance to power supply terminals, the safety ground is a completely separate circuit which normally carries no current.
In modern installations (with diff current protection) any current in the ground wire above a certain threshold leads to immediate circuit breaker tripping. This protects the person who somehow managed to touch a live wire, like in your example. The only way to get shocked without tripping the protection would be to touch both hot and neutral wires, while NOT touching the ground.
In older installations, ground wire is simply connected to conductive parts which could be touched, like metal cases (most often TN-S earthing, but other earthing systems exist). This guarantees that metal cases can't go live without provoking a prompt short circuit. Of course, if you open the case and manage to touch a live wire inside, there will be nothing to protect you.
You cannot rely on an AC mains or high voltage DC feed being isolated. For this reason, any exposed metal (conductive) parts should be earthed because, if an internal wiring fault developed that connected "live" to those exposed metal parts, the fuse (yes a fuse or breaker is required for electrocution prevention) will blow and the live is disconnected upstream.
The fuse is much "weaker" than the ground wire so, after a short period of a few milli seconds the fuse blows and the device becomes safe. In that short period of time you can receive a small shock but probability suggests that this is an unlikely event.
A floating AC supply isn't that safe even to the touch due to capacitance to ground - a decent "tingle" can usually be felt.
If the device is powered by mains it is always somehow related to the ground. No absolute floating potential is possible unless is battery powered, even then there is always a finite isolation strenght capability. At some voltage the isolation breaks, always. The grounding is connected to the metal case, you should make a new sim, and if a faulty component touches the case, the current is sinked into a ground, your body would be just a parallel circuit with much higheer impedance than a wire.
And secondly does connecting any point in a circuit to the earth ground pull the voltage in that point to the ground level ?
The safety earth provides protection against faults where a component in the equipment is not acting as it was originally designed. Some fault conditions may be made more dangerous by the presence of the safety earth, but in general a safety earth will be designed to detect latent failures before a dangerous situation occurs.
It is true that a human body needs to be exposed to two parts of a circuit before electrocution can occur. The intention of a safety earth is to prevent even one past of the external (touchable) equipment bridging to the live circuit - stopping the problem before it becomes fatal. These practices are designed by analyzing hundreds and thousands of real-life failure conditions.