Am I understand right? As I know, there are two requirments of current existing - closed conductor and potential difference. I heared that the current flows on the part of circle with lowest resistence.So, on the picture, I've pinned showed a circle. In normal case(when resistor is ok) it flows from +, through resistor, to -, and completely don't flows to ground, yes? In another case, when there is no resistance(but circle is closed), as I understand it should completely flow to ground. Ground(Earth) have some potential(+ or -, I don't know), but it doesn't equals to curent circle potential. So it should flow from wire, but the wire comes to be unclosed in this case, so why it flows to ground? All of free electrons should flow out from wire, no? The same as for me - why current will flows from wire to me, and then to the ground? If I will not touch the ground, the current will not flows throught me?
As I know, there are two requirments of current existing - closed conductor and potential difference.
This is essentially correct.
I heared that the current flows on the part of circle with lowest resistence.
This isn't really correct. If a potential is applied across a resistive device, a current will flow through that device, regardless of what other paths exist in the circuit. It is common that connecting too low a resistance across a voltage source will cause the source's voltage to drop, which would reduce the current through other devices connected to the source. But if the source is strong enough to maintain its voltage, current flows through all paths, not just through the lowest-resistance path.
Ground(Earth) have some potential(+ or -, I don't know), but it doesn't equals to curent circle potential.
Ground is the node in a circuit that we define to have a potential of 0.
Sometimes this node is actually connected to the earth, but not always.
The same as for me - why current will flows from wire to me, and then to the ground?
This will happen if one of the terminals of the voltage source is connected to ground, which is a very common arrangement, and you contact the other terminal.
Even in mains wiring, typically one of the two wires is connected to an earth ground. So touching the other ("hot") wire while your feet are touching the earth means applying the mains voltage across your body, which is very hazardous.
If I will not touch the ground, the current will not flows throught me?
If you don't touch both terminals (one of which might be ground) of the voltage source (or other wires connected to those terminals) at the same time, then you will not be shocked.
But even if you wear rubber shoes, for example, there is still a capacitance between your body and the earth. So if you contact the hot wire of mains, you might feel a tingle due to small currents that can flow through you and the parasitic capacitor to earth. (Don't experiment with this just for fun)