harmonic oscillations are described with this equation: y=y0*sin(omega*t+phi0).
In this case, omega=sqrt(k/m), on the other side, omega = 3.85 rad/s. So you can find k.
as the energy of the system is constant:
k*(y0)^2=m(vmax)^2.
From this equation you can find the maximum velocity.
I think it's not the best idea to solve this task using energy and work. Maybe it would be easier to use the 1-st Newton's law (for solving the b) task):
the friction forse is: mu*(Mg-k*x*sin(theta)), and it is equal to k*x*cos(theta)