How is the electric field inside a hollow conducting sphere zero? If we put a charge inside the cavity of a hollow conducting sphere, the charge will create an electric field and so the negative charges will move close to the cavity. This will create a shortage of negative charges at the surface of the sphere, creating an overall positive charge at the surface. My question is: now the surface has positive charge distribution, and around the cavity there is a negative charge distribution. How can the electric field still be zero in this case? I draw a sketch to illustrate what I mean:

 A: The electric field in the cavity is not zero. Inside the cavity it is as you have drawn it.
I recommend that you use a textbook to check the argument for the absence of an electric field in a cavity in a conductor. You will see that it fails if there are charges suspended in the cavity.
Your diagram also seems to show a field inside the conductor itself. That would mean that free charges would be moving. So we wouldn't have a steady state.
Your radially inward arrows inside the conductor show the field contribution due to the induced charges on the inner and outer surfaces of the conductor. But there will also be  an outward-pointing field contribution inside the conductor due to the charge suspended in the cavity. In the steady state these two field contributions inside the conductor cancel to zero.
A: Your diagram is not complete.
The $+q$ charge induces negative charges on the inside of the conducting shell and an equal number of positive charges on the outside of the spherical shell as shown in the digram below.

The $+q$ charge produces a radial electric field (blue) and the induced charges produce a field (red) inside the conductor exactly in opposition to the radial field produced by the charge $+q$.
The net result (green) is a radial field inside the shell, no electric field within the conducting shell, and a radial field outside the conducting shell.
