As like Earth, does the moon have a day (24 hours). If it has, how many hours are in a moon day?.
The answer depends on your definition of a day.
If you define a day as we usually define it in the Earth (time between the Sun is at noon or average time between sunrises, a 24 hours day in Earth), the length of a day in the Moon is the synodic period of the Moon and it takes 29.530589 days (29 d 12 h 44 min 2.9 s).
Anyway, if you define a day as rotation on own axis, that is, time between a far away star being at noon, you have what in Earth is called sidereal day (23 hours, 56 minutes in Earth). In the moon the day defined this way would be 27.321661 days (27 d 7 h 43.19 min 11.5 s).
Please notice that since the Moon is tidally locked to the Earth, rotation periods equal orbital periods.
Defining that a day is a rotation on the axis, 1 moon day is approximately equal to 27.3 Earth days. This link on moon rotation may interest you.