Why we define Stellar motions with respect to sun? We take observations from earth but to define radial velocity, transverse velocity and the proper motion of stars, why we consider them with respect to the sun? and then we do some corrections due to both rotational and orbital motion of the earth.

Why can't we directly consider these motions with respect to earth instead of Sun?

And what is the whole procedure of correction?
The Earth is a moving (actually, accelerating) platform from which we make our observations. If you want to describe the motion of a distant celestial body, then it does not make much sense to provide a geocentric velocity, because this will depend on exactly when the observations were taken (because the Earth orbits with a speed of about 30 km/s, but the velocity changes throughout the year), the position on the Earth that the measurement was taken (because the Earth's equator revolves at around 0.5 km/s, but this is different at different latitudes) and the position of the star in the sky (because the previous two effects have to be resolved in the direction of the star).

Given that, then it is far easier to quote a velocity in a frame of reference that does not depend on these things. One can use the heliocentric frame in most circumstances - that is the frame of reference in which the Sun is stationary. To do this, one has to remove the components of the Earth's orbital and rotational velocity. However, if very precise measurements are being done then it is better to use the barycentric reference frame, which is with respect to the centre of mass of the solar system (since the Sun orbits this with a speed of around 0.1 m/s).