How the current from circuit cross a capacitor dielectrics?
The current does not flow through the capacitor in the sense that an electron goes in on one side and comes out on the other side. The dielectric prevents this.
What does happen is that an electron on one plate of the capacitor forms a negative charge. This negative charge attracts a positive charge on the other plate of the capacitor. In other words, it repels an electron on the other plate.

Current is simply movement of charge / electrons.

A DC current is movement of charge in one direction (not possible through a capacitor).

An AC current is movement of charge alternating in opposite directions (possible through a capacitor).