opposes the relative motion of the disk with respect to the platform
If the platform is spinning clockwise, then the relative motion of the disk relative to the platform is counterclockwise... while the force on the disk is clockwise. So yes, that is true.
And as long as the string is attached at the center, it is always pointing radially outward - so the direction of the friction is always perpendicular to the direction the string is pointing. As a result there is no component of the friction along the string.
This means that the only force that is capable of breaking the string is the centripetal force due to the disk. This means you have to solve the question "at what rate of rotation is the centripetal force on a 3 kg object at the end of a 1 m string equal to 100 N?". This happens when
$$\rm F = m\omega^2 r = 100~N$$
With a coefficient of kinetic friction of 0.1, the (linear) acceleration of the mass will be 0.1 g (where g is the acceleration due to gravity, 9.81 m/s$^2$).
Finally, you know that $v = \omega r$. Now you have everything you need to solve this.
This diagram helps to explain why the force on the disk due to friction is perpendicular to the string:
The disk is rotating (slower than the platform). If we look at things in a rotating frame of reference (moving so the disk is stationary), we see the platform is still rotating underneath the disk. The motion of the platform right below the disk is perpendicular to the radial vector (from the center to the disk) and thus the force of friction on the disk will be perpendicular as well.
If you consider the disk is not an infinitesimal point, then there will be points to the left and right where the force is not quite perpendicular to the string - but to the extent there is a force on one side that points out, there is an equal force on the other side that points in. This does leave a small residual torque on the disk: I'm pretty sure that the person asking the question is not asking you to think about that (although it does matter - as the disk starts to rotate about the center of the platform, it also ends up with a rotation about its own center... otherwise the attachment point could not continue to point inwards).