Cartesian angular velocity (Rate of change of Quaternion to Rate of change of Euler angle)

Hello everyone I have cartesian linear(x,y,z) & angular velocity(qx,qy,qz,qw). To drive the robot i found 2 solutions either use joint velocities or joint values. 1) How can I convert cartesian velocities to joint velocities ? 2) I found moveit function setFromDiffIK but for this i need angular velocity in euler but i have in quaternion. How can i convert rate of change of Quaternion to rate of change of Euler angle? Thanks in advance...