The electric field inside a conductor must be zero. Can this be explained with the help of Gauss's law?
Also, how does this explain that if we have a conducting sphere with a cavity inside, and we place a point charge (say positive, at the centre of this cavity) then there is a negative charged induced on the inner surface of this sphere, and a positive charge induced on the outer surface of the sphere?
Yes it can be explained using gauss's law, if you assume that charge on conductors reside on its surface.
You could take a random gaussian surface inside the conductor and use gauss's law i.e. $$\oint \vec E \cdot d \vec A = \cfrac{q_{inside}}{\epsilon_0}$$ Since all the charge on the conductor resides on surface of the conductor $q_{inside} = 0$. $$\therefore \oint \vec E \cdot d \vec A = \cfrac{0}{\epsilon_0} = 0$$ Since area of conductor isn't zero $\vec E = 0$.
