Does the niece inherit from a married paternal uncle who has no children? And what is the reason for that?

The niece does not inherit from her uncle if he has an heir who takes the wealth, because she is not among the Ashab al-Furood (Qur'anic heirs) nor the 'Asabat (agnatic heirs), but rather among the Dhawu al-Arham (relatives by blood, but not qualifying as Qur'anic or agnatic heirs). However, if the uncle dies and leaves no one but his niece and his wife, then she inherits the remainder after the wife's share (one-fourth), by placing her in the position of her father. This is the view of the proponents of Tanzeel (analogy/substitution) regarding the inheritance of Dhawu al-Arham.