What are centripetal forces for flywheel precession movement? 
What are centripetal forces for this flywheel? I suppose for rotation around "inner" axis centripetal force is due to attractive forces between particles inside flywheel. However what about rotation around outer axis? Static friction? If yes, why its direction is centripetal and not centrifugal, when G-force has tendency to rotate flywheel clockwise with respect to point of contact with ground?
 A: The force $G\sin(\theta)$ creates a torque that, on its own, would tend to rotate the spinning axis about the point where the top touches the table. This adds a torque to an object that already has significant angular momentum. This added torque, by $\tau = d ~ G\sin = J \vec{\alpha}$ adds it’s angular momentum, $M$ in the figure, by the right hand rule of $\vec{d} \times \vec{G}$. That $M$ is being added the existing angular momentum vector $L$. The vector sum moves $L$ to $L+dL$ as shown. But the direction of $M$ keeps changing. So even though there is an apparent rotation in the precession motion, it is part of a larger $\omega$. It does not need a centripetal force because it is not a simple revolution (in fact we just analyzed the changing angular momentum vector). That provides the precession. And $M$ will continue to result in the tangential motion as shown.
One way to (very loosely) think of it is that the gyroscopic force is providing the centripetal resistance. But the above description is more rigorous as we can see how the momentum vectors add. To gain better intuition, see this and related about precession and/or gyroscopes:  https://youtu.be/ty9QSiVC2g0
