Yes, the charging power is determined by the charging device, the power of the charger only means that the charger can achieve the maximum charging power, does not mean that it will be used to charge will reach this power.
First of all, how much fast charging will definitely damage the capacitor pen, fast charging has more current and more heat, I think heat is the primary factor that will cause damage to the battery, the battery capacity is very small, large current charging will also cause a certain impact.