The angular velocity of the earth around the sun increases, when it comes closer to the sun?

Yes, linear velocity as well as angular velocity increase as the earth approaches the point of nearest distance to the sun. This is a direct consequence of the planets' obediently abiding by Kepler's 2nd Law ;) , which postulates constant areal velocity, meaning that In a small time dt the planet sweeps out a small triangle having base line r and height r dθ and area dA = 1/2 * r * r dθ and so the constant areal velocity is

dA / dt = 1/2 r² dθ/dt .

[ en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion ]