Is it permissible to pay all or part of the annual Zakat on money to a orphaned niece if her deceased father's pension is sufficient and her basic needs are met?

As long as your niece is financially secure, she is not eligible to receive zakat. Zakat is only distributed to the eight categories of recipients. An orphan who is not poor or needy does not receive zakat simply because they are an orphan. If she is poor and you are her heir, her maintenance is obligatory upon you, and it is not permissible to pay your zakat to her.