Does half wave in dipole means that duration of 1/4 of a one signal cycle should equals capacitor charging duration, if we consider that dipole is a capacitor?
Dipole antenna is not just a capacitor - it also has distributed inductance and resistance - but we can still assess its charge time and discuss how this time is related to the dipole cycle.
Let's say, we applied a step voltage to the terminals of a dipole, assuming that terminals are in the middle of the dipole (center fed dipole). A positive and a negative waves will start moving outwards and, in certain time, will reach the ends of the dipole.
If we stop the clock right there (i.e., without waiting for the waves to reflect multiple times and settle), we can say that this is the charge time of the dipole capacitance and, since the velocity of these charge waves is the same as the velocity of the charges in an oscillating dipole, we can say that this time corresponds to the quarter of the dipole cycle.