Is the plane in which Moon orbits around earth, inclined with respect to earth's equatorial plane? If yes, is it constant or does it change with time? If it changes, how much time does it take to make a complete circle around earth?
Indeed, the moon's orbital plane is inclined with respect to the earth's equatorial plane, and this inclination changes over time: the angle between both planes varies between 28°36′ and 18°20' with a period of approximately 18.6 years.
This is the combination of the 23°27′ inclination of Earth's equatorial plane with respect to the ecliptic (precession period ~26000 years), and the 5°09' inclination of the Moon's orbit with respect to the ecliptic (precession period ~18.6 years).
Since the precession period of Earth's equatorial plane can be considered negligible compared to that of the Moon's orbital plane, we can just say that the angle between the Moon's orbital plane and Earth's equatorial plane changes with a period of approximately 18.6 years.
You can find more find more information on this topic in Wikipedia's Orbit of the Moon; Inclination to the equator and lunar standstill.
Above: Lunar orbit and orientation with respect to the Ecliptic, showing the values of all relevant angles. (source)