Question

Why mechanical energy and angular momentum remains constant when earth revolves around the sun

Answer 1

The Earth does lose or gain energy due to multiple phenomena-

Space isn't a perfect vacuum. It’s density is about 0.1 to 1000 atoms per cubic cm. This leads to frictional and pressure drag losses.

Cosmic radiations emitted from distant stars, gamma ray bursts, supernovae, etc., made of high energy particles such as protons, helium nuclei and other particles constantly hit our planet, slightly altering its orbital velocity.

Solar particles such as ions, and to a lesser extent high energy protons, are emitted by the solar flares of the sun and alter the Earth's dynamics upon impact.

Meteoric particles originating from the origins of the solar system also constantly hit our planet transferring their kinetic energy and also slightly altering the Earth's dynamics.
The light itself emitted by the sun or other distant celestial events also has an impact through a phenomenon called radiation pressure.