I have a schematic and I can see diffrent symbol of condensator.
Most of the world calls them capacitors.
I am also working with Fritzing which is an opensource PBC maker.
I think you mean PCB.
I don't understand what you mean "different representation." The schematic symbol is the same for C1, C2, and C3. The only difference is the capacitance value.
Also, is it true that the Output pin of U2 (VCC) has to be "wired" to the the Resistor R2 (VCC) in my PBC?
R2 is not connected to VCC. It is connected to Vbatt which is completely different from VCC.
I suppose that C19 has a polariry and why C10 has a smaller bar.
C19 is an polarized electrolytic capacitor (generally aluminum) and C10 is a non-polarized capacitor (ceramic).
With Fritzing, I can select a condensator which show a voltage. Why voltage are not show in the linked shematic?
Capacitors have a rated voltage. You should select a capacitor with a voltage rated higher than the voltages it will see in the circuit. Knowing this, there isn't much need for calling out a rated voltage on those simple schematics.