What is the fate of the money saved by the questioner, which was designated for his niece's marriage, and is it permissible to continue saving it and consider it part of the zakat, knowing that the questioner will cover all marriage expenses from his own money?

The condition for Zakat is that it must be transferred to its rightful recipient. The Zakat you have set aside for your nieces' dowries remains a debt upon you and must be paid immediately. It is permissible to give it to your sister and her daughters if they are eligible to receive Zakat. It can be delivered through their father.

What was given to the father to help him with expenses is not considered Zakat.

The fundamental principle is that Zakat must be paid immediately; it is not permissible to save it for your nieces' future dowries.

It is permissible to spend Zakat on furnishing a poor woman, and on purchasing wedding necessities without extravagance. You may spend your Zakat on furnishing your nieces as long as their maintenance is not obligatory upon you.